有哪些很难的数学题，答案是 629，宿舍当门牌用？

发布时间：

2024-11-12 17:08

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大佬们在默默地注视着我

$\displaystyle{- \frac{\int\limits_{0}^{1} \left(-3774\right)\, dx + \int\limits_{0}^{1} \left(- 1890 \cos{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 6 \sin{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 3 \sin{\left(x^{2} \right)} {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4} \end{matrix}\middle| {- \frac{1}{4}} \right)}\right)\, dx + \int\limits_{0}^{1} \cos{\left(x^{2} \right)} {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4} \end{matrix}\middle| {- \frac{1}{4}} \right)}\, dx + \int\limits_{0}^{1} 2 {{}_{1}F_{2}\left(\begin{matrix} \frac{3}{4} \\ \frac{3}{2}, \frac{7}{4} \end{matrix}\middle| {- \frac{1}{4}} \right)}\, dx + \int\limits_{0}^{1} 3 {{}_{1}F_{2}\left(\begin{matrix} \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4} \end{matrix}\middle| {- \frac{1}{4}} \right)}\, dx}{3 \left({{}_{1}F_{2}\left(\begin{matrix} \frac{1}{4} \\ \frac{1}{2}, \frac{5}{4} \end{matrix}\middle| {- \frac{1}{4}} \right)} + 2\right)}}\\$

啥，不是很难？来，上家伙：

$\displaystyle{- \frac{i \left(\int\limits_{0}^{1} \left(- 3160096 i\right)\, dx + \int\limits_{0}^{1} \left(- 1582560 i \cos{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 1260 \sqrt[4]{-1} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 1260 \sqrt[4]{-1} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \cos{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 5024 i \sin{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 1260 \sqrt[4]{-1} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \sin{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} 4 \left(-1\right)^{\frac{3}{4}} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}\, dx + \int\limits_{0}^{1} 4 \left(-1\right)^{\frac{3}{4}} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \cos{\left(x^{2} \right)}\, dx + \int\limits_{0}^{1} \left(- \pi^{3} {{G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}^{2} \sin{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} 4 \left(-1\right)^{\frac{3}{4}} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \sin{\left(x^{2} \right)}\, dx + \int\limits_{0}^{1} i \pi^{3} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \sin{\left(x^{2} \right)}\, dx + \int\limits_{0}^{1} \left(- \pi^{3} {{G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}^{2} \cos{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \left(- 2 \pi^{3} {{G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}^{2}\right)\, dx + \int\limits_{0}^{1} \left(- i \pi^{3} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} \cos{\left(x^{2} \right)}\right)\, dx + \int\limits_{0}^{1} \pi^{3} {{G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}^{2}\, dx + \int\limits_{0}^{1} \left(- 3 i \pi^{3} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}\right)\, dx\right)}{-5024 + 1260 \left(-1\right)^{\frac{3}{4}} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} + i \pi^{3} {{G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}^{2} + 4 \sqrt[4]{-1} \pi^{\frac{3}{2}} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} + \pi^{3} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{1}{4} & 0, \frac{3}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)} {G_{1, 3}^{1, 0}\left(\begin{matrix} & 1 \\\frac{3}{4} & 0, \frac{1}{4} \end{matrix} \middle| {- \frac{1}{4}} \right)}}}\\$

两天不见，破两百赞了？

行行行，再补一个

假设你的门牌号是为厕所配的，那么你可以把这个挂你门牌号上面：

$\displaystyle{\int\limits_{0}^{114514} \frac{2 x^{2} \left(x - 1\right)^{2} \left(- x \left(4 \sqrt{3} \pi + \ln{\left(a \right)} + b - 3 \sqrt{3} i \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} - 3 \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)} - 3 \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} + 3 \sqrt{3} i \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)}\right) - \ln{\left(a \right)} + 4 \sqrt{3} \pi + c - 3 \sqrt{3} i \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} + 3 \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} + 3 \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)} + 3 \sqrt{3} i \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}{\left(x^{3} + 1\right) \left(- \ln{\left(a \right)} + 4 \sqrt{3} \pi + c - 3 \sqrt{3} i \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} + 3 \ln{\left(\frac{229027}{2} - \frac{\sqrt{3} i}{2} \right)} + 3 \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)} + 3 \sqrt{3} i \ln{\left(\frac{229027}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\, dx}$

其中：

$\begin{cases} a &=& 25864081383828928548573352858496978085664783688812232174971088904775875562713886528163247043608301359157621860504150390625\\ b &=& 118016977599\\ c &=& 9009809896822188\\ \end{cases}\\$

不是，我刚更新完一个小时，怎么就三百了？！是大佬们举荐了我吗！

针对Python人士的题目（可能违反了题目要求）：

下列表达式的值为多少？禁止使用计算机和计算器。

"".join( map( chr, [ ( lambda *_: ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[2] ) ) + (_[0] & _[3]) * ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[4] ) ) + (_[0] & _[5]) * (_[0] << ((_[0] << _[0]) + _[0] & _[3])) + (_[0] & _[6]) * (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[7]) * (_[0] << _[0]) + _[0] & _[8] )(1, 2, 5, 3, 4, 6, 13, 27, 54), ( lambda *_: ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[2] ) ) + (_[0] & _[3]) * ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[4] ) ) + (_[0] & _[5]) * (_[0] << ((_[0] << _[0]) + _[0] & _[3])) + (_[0] & _[6]) * (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[7]) * (_[0] << _[0]) + _[0] & _[8] )(1, 2, 5, 3, 4, 6, 12, 25, 50), ( lambda *_: ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[2] ) ) + (_[0] & _[3]) * ( _[0] << ( (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[1]) * (_[0] << _[0]) + _[0] & _[4] ) ) + (_[0] & _[5]) * (_[0] << ((_[0] << _[0]) + _[0] & _[3])) + (_[0] & _[6]) * (_[0] << ((_[0] << _[0]) + _[0] & _[1])) + (_[0] & _[7]) * (_[0] << _[0]) + _[0] & _[8] )(1, 2, 5, 3, 4, 7, 14, 28, 57), ], ) )

四百赞纪念

给个小一点的，适合挂在门派上面，但计算量依旧不少的：

$\displaystyle{\int\limits_{0}^{1} \frac{6 x \left(3 - \log{\left(16 \right)}\right) - \log{\left(1152921504606846976 \right)} + 2557}{6 \left(3 - \log{\left(16 \right)}\right) \left(\sqrt[3]{x} + 1\right)^{2}}\, dx}$

然后再来一个（停不下来了）：

$\displaystyle{\int\limits_{0}^{1} \frac{x \log{\left(\frac{4096}{729} \right)} - \sqrt{3} \pi + \log{\left(\frac{2153693963075557766310747}{281474976710656} \right)} + 5643}{3 \left(\left(\sqrt{x} + 1\right)^{3} + 1\right) \log{\left(\frac{16}{9} \right)}}\, dx}$

再来：

$\displaystyle{\int\limits_{0}^{1} \frac{x^{2} \log{\left(\frac{4096}{729} \right)} + \sqrt{3} \pi + \log{\left(\frac{a}{b} \right)} + 5574}{3 \left(\left(\sqrt{x} + 1\right)^{3} + 1\right) \log{\left(\frac{16}{9} \right)}}\, dx}$

（其中 $\begin{cases} a &=& 1093061682616768598101980749118434678309602685816438255039403134728775682721408160470718926107\\ b &=& 6277101735386680763835789423207666416102355444464034512896 \end{cases}\\$ ）

再来：

$\displaystyle{\int\limits_{0}^{1} \frac{x^{3} \log{\left(\frac{1099511627776}{3486784401} \right)} + \log{\left(\frac{a}{b} \right)} + 17853}{10 \left(\left(\sqrt{x} + 1\right)^{3} + 1\right) \log{\left(\frac{16}{9} \right)}}\, dx}$

（其中

$\begin{cases} a &=& 772657434874056687988804911108631000425180089641585565491987815965830802151971312647570018221250060545096915733431805822246262588742147770433024105582582512846305890491627989606446801829775242537001324433241459535959757837214441969241037588040654527579393599147988983099810515228690442870534218927553617042712669520871660456732484354687175768900044477002145502285773139914335834594491650009772787459809349628172803369261909075144592306612096066663221710102114436999628477993393941823350580462456870905800031027735717997638332839700214096824301637779415641975015533575153966189771214564719551399882464606038878742628034514397174363177510731541250160308263432511573490005382293577079746864631738166619419132130083802405083325964792873144328657328541570758517918942363048894957099218895461568420574514796255938455576148807053117791222768352238240521127469540324116879997922084310476933578822632932642937521664833215066619821585368421221950953623175505155886217126881005544357519414419527975443256726201574637990124411592967604875201226743300591196693276345460348155058724891772760005096591369619012828760440905416322666054542791196332215922123410049915377654951703442251842683556300086694790174601419266777784978801\\ b &=& 433300210274926779301235722995130529126851924312253566276831366547097655953268278873591999368453759375352459120642109169274240110620843517970102311224458427564046616227161115801662152359395451958893835480905010246703239443701925453743683726938789767940577524555724362397039358587448248740993955708382317083531851133758531532844694304737183093418571190053292997716413815714417740434254315670267335553209606545389900958653541702218767662872949109999460596999125719155768466778443229719919179735890978537026576050107500869340314188887101095263339865901080787145771915722368720844521851040375582291274824574444462419841916186875058374404329003250698574832235855871168399140082282900718430116575617097058691735266917705341386171618452673063526784039252631042036988932549246976 \end{cases}\\$ ）

积分用光了公式，那么就来玩求和

先是一碟开胃小菜：

$\displaystyle{\sum_{k=0}^{\infty} \frac{1258 \tanh{\left(\pi \right)}}{\left(k^{2} + 1\right) \left(\tanh{\left(\pi \right)} + \pi\right)}}$

然后：

$\displaystyle{\sum_{k=0}^{\infty} \frac{144058612 \tanh{\left(\sqrt{114514} \pi \right)}}{\left(k^{2} + 114514\right) \left(\tanh{\left(\sqrt{114514} \pi \right)} + \sqrt{114514} \pi\right)}}$

$\displaystyle{\sum_{k=0}^{\infty} \left(\frac{- \frac{\pi}{\tanh{\left(\pi \right)}} + 1257}{2 \cosh{\left(1 \right)} \left(2 k\right)!} + \frac{1}{k^{2} + 1}\right)}$

$\displaystyle{\sum_{k=0}^{\infty} \left(\frac{- \left(\tanh{\left(\pi \right)} + \pi\right) \sqrt{\tanh^{2}{\left(\pi \right)} + 2 \pi \tanh{\left(\pi \right)} + \pi^{2} + 10064 \cosh{\left(1 \right)} \tanh^{2}{\left(\pi \right)}} + \tanh^{2}{\left(\pi \right)} + 2 \pi \tanh{\left(\pi \right)} + \pi^{2} + 5032 \cosh{\left(1 \right)} \tanh^{2}{\left(\pi \right)}}{8 \cosh^{2}{\left(1 \right)} \tanh^{2}{\left(\pi \right)} \left(2 k\right)!} + \frac{\sqrt{2} \sqrt{- \left(\tanh{\left(\pi \right)} + \pi\right) \sqrt{\tanh^{2}{\left(\pi \right)} + 2 \pi \tanh{\left(\pi \right)} + \pi^{2} + 10064 \cosh{\left(1 \right)} \tanh^{2}{\left(\pi \right)}} + \tanh^{2}{\left(\pi \right)} + 2 \pi \tanh{\left(\pi \right)} + \pi^{2} + 5032 \cosh{\left(1 \right)} \tanh^{2}{\left(\pi \right)}}}{4 \left(k^{2} + 1\right) \cosh{\left(1 \right)} \tanh{\left(\pi \right)}}\right)}$

一、 $\displaystyle{\sum_{k=0}^{\infty} - \frac{2516 - 2516 \cosh{\left(2 \pi \right)}}{\left(k^{2} + 1\right)^{2} \left(-2 + 2 \pi^{2} + 2 \cosh{\left(2 \pi \right)} + \pi \sinh{\left(2 \pi \right)}\right)}}$

二、 $\displaystyle{\sum_{k=0}^{\infty} \frac{10064 \sinh^{3}{\left(\pi \right)}}{\left(k^{2} + 1\right)^{3} \left(3 \pi^{2} \sinh{\left(\pi \right)} + 2 \pi^{3} \cosh{\left(\pi \right)} + 8 \sinh^{3}{\left(\pi \right)} + 3 \pi \sinh^{2}{\left(\pi \right)} \cosh{\left(\pi \right)}\right)}}$

三、 $\displaystyle{\sum_{k=0}^{\infty} \frac{483072 \sinh^{4}{\left(\pi \right)}}{\left(k^{2} + 1\right)^{4} \left(- 30 \pi \sinh{\left(2 \pi \right)} - 60 \pi^{2} + 32 \pi^{4} + 60 \pi^{2} \cosh{\left(2 \pi \right)} + 48 \pi^{3} \sinh{\left(2 \pi \right)} + 16 \pi^{4} \cosh{\left(2 \pi \right)} + 15 \pi \sinh{\left(4 \pi \right)} + 384 \sinh^{4}{\left(\pi \right)}\right)}}$

四、 $\displaystyle{\sum_{k=0}^{\infty} \frac{483072 \tanh^{5}{\left(\pi \right)}}{\left(k^{2} + 1\right)^{5} \left(- 40 \pi^{5} \tanh^{2}{\left(\pi \right)} - 80 \pi^{4} \tanh^{3}{\left(\pi \right)} - 90 \pi^{3} \tanh^{4}{\left(\pi \right)} - 105 \pi^{2} \tanh^{5}{\left(\pi \right)} + 105 \pi \tanh^{4}{\left(\pi \right)} + 384 \tanh^{5}{\left(\pi \right)} + 105 \pi^{2} \tanh^{3}{\left(\pi \right)} + 20 \pi^{4} \tanh^{5}{\left(\pi \right)} + 90 \pi^{3} \tanh^{2}{\left(\pi \right)} + 16 \pi^{5} \tanh^{4}{\left(\pi \right)} + 60 \pi^{4} \tanh{\left(\pi \right)} + 24 \pi^{5}\right)}}$

一、 $\displaystyle{\sum_{k=0}^{\infty} \frac{\sqrt{1 - \frac{1258}{{{}_{0}F_{2}\left(\begin{matrix} \\ \frac{1}{3}, \frac{2}{3} \end{matrix}\middle| {\frac{1}{27}} \right)}} + \frac{395641}{{{{}_{0}F_{2}\left(\begin{matrix} \\ \frac{1}{3}, \frac{2}{3} \end{matrix}\middle| {\frac{1}{27}} \right)}}^{2}}} + 1}{\Gamma\left(3 k + 1\right)}}$

二、 $\displaystyle{\sum_{k=0}^{\infty} \frac{\sqrt{1 - \frac{1258}{{{}_{0}F_{4}\left(\begin{matrix} \\ \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5} \end{matrix}\middle| {\frac{1}{3125}} \right)}} + \frac{395641}{{{{}_{0}F_{4}\left(\begin{matrix} \\ \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5} \end{matrix}\middle| {\frac{1}{3125}} \right)}}^{2}}} + 1}{\Gamma\left(5 k + 1\right)}}$

三、 $\displaystyle{\sum_{k=0}^{\infty} \frac{\sqrt{1 - \frac{1258}{{{}_{0}F_{5}\left(\begin{matrix} \\ \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6} \end{matrix}\middle| {\frac{1}{46656}} \right)}} + \frac{395641}{{{{}_{0}F_{5}\left(\begin{matrix} \\ \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6} \end{matrix}\middle| {\frac{1}{46656}} \right)}}^{2}}} + 1}{\Gamma\left(6 k + 1\right)}}$

四、 $\displaystyle{\sum_{k=0}^{\infty} \frac{\sqrt{1 - \frac{1258}{{{}_{0}F_{6}\left(\begin{matrix} \\ \frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7} \end{matrix}\middle| {\frac{1}{823543}} \right)}} + \frac{395641}{{{{}_{0}F_{6}\left(\begin{matrix} \\ \frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7} \end{matrix}\middle| {\frac{1}{823543}} \right)}}^{2}}} + 1}{\Gamma\left(7 k + 1\right)}}$

五、 $\displaystyle{\sum_{k=0}^{\infty} \frac{\sqrt{1 - \frac{1258}{{{}_{0}F_{7}\left(\begin{matrix} \\ \frac{1}{8}, \frac{1}{4}, \frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}, \frac{7}{8} \end{matrix}\middle| {\frac{1}{16777216}} \right)}} + \frac{395641}{{{{}_{0}F_{7}\left(\begin{matrix} \\ \frac{1}{8}, \frac{1}{4}, \frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}, \frac{7}{8} \end{matrix}\middle| {\frac{1}{16777216}} \right)}}^{2}}} + 1}{\Gamma\left(8 k + 1\right)}}$

再来一个特殊函数的：

$\displaystyle{\sum_{k=0}^{\infty} \frac{1258}{\left(- J_{0}\left(2\right) + I_{0}\left(2\right)\right) \Gamma^{2}\left(2 k + 2\right)}}$

$\displaystyle{\sum_{k=0}^{\infty} \frac{- 2 k J_{0}\left(2\right) + 2 k I_{0}\left(2\right) - I_{1}\left(2\right) - J_{1}\left(2\right) - J_{0}\left(2\right) + I_{0}\left(2\right) + 2516}{2 \left(- J_{0}\left(2\right) + I_{0}\left(2\right)\right) \Gamma^{2}\left(2 k + 2\right)}}$

尝试把超几何移到分母那里：

$\displaystyle{\sum_{k=0}^{\infty} \frac{629 \cdot 2^{- 2 k} \sqrt{\pi}}{2 \Gamma\left(k + \frac{3}{2}\right) \Gamma\left(2 k + 2\right) {{}_{0}F_{2}\left(\begin{matrix} \\ \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {\frac{1}{16}} \right)}}}$

尝试把超几何函数的参数补齐：

$\displaystyle{\sum_{k=0}^{\infty} \frac{629 \Gamma\left(3 k + 2\right)}{\Gamma^{2}\left(2 k + 2\right) {{}_{2}F_{2}\left(\begin{matrix} \frac{2}{3}, \frac{4}{3} \\ \frac{3}{2}, \frac{3}{2} \end{matrix}\middle| {\frac{27}{16}} \right)}}}$

突然想到还可再加一些特殊函数的，比如：

$\displaystyle{\sum_{k=0}^{\infty} \frac{3^{- k} \left(- 3^{k} \log{\left(27 \right)} - 6 \cdot 3^{k} \operatorname{Chi}\left(\frac{\sqrt{3}}{3}\right) + 6 \cdot 3^{k} \gamma + 1252 \cdot 3^{k} + 6 \cdot 3^{k + \frac{1}{2}} \sinh{\left(\frac{\sqrt{3}}{3} \right)} - 2 \sinh{\left(1 \right)} - 2 \gamma + 2 \operatorname{Chi}\left(1\right) + 2\right)}{4 \left(k + 1\right) \left(- \sinh{\left(1 \right)} - \gamma + \operatorname{Chi}\left(1\right) + 1\right) \Gamma\left(2 k + 4\right)}}$

大杂烩：

$\displaystyle{\sum_{k=0}^{\infty} - \frac{2^{- k} \left(\left(-1\right)^{k} 2^{k + 1} \gamma + \left(-1\right)^{k} 2^{k + \frac{3}{2}} \sinh{\left(\frac{\sqrt{2}}{2} \right)} + \left(-1\right)^{k + 1} \cdot 2^{k} \log{\left(2 \right)} + 627 \left(-2\right)^{k} + \left(-2\right)^{k + 1} \operatorname{Chi}\left(\frac{\sqrt{2}}{2}\right) - 1 - \operatorname{Ci}{\left(1 \right)} + \gamma + \sin{\left(1 \right)}\right)}{2 \left(k + 1\right) \left(- \sin{\left(1 \right)} - \gamma + \operatorname{Ci}{\left(1 \right)} + 1\right) \Gamma\left(2 k + 4\right)}}$

尝试把π、ℯ和γ全部整进去：

$\displaystyle{\sum_{k=0}^{114514} \frac{- 4 \left(-1\right)^{k} 2^{- 2 k} \sqrt{\pi} e^{k} \operatorname{Chi}\left(1\right) \Gamma\left(2 k + 1\right) + 4 \left(-1\right)^{k} 2^{- 2 k} \gamma \sqrt{\pi} e^{k} \Gamma\left(2 k + 1\right) + \Gamma\left(k + \frac{1}{2}\right) {{}_{3}F_{3}\left(\begin{matrix} 1, 1, 1 \\ \frac{3}{2}, 2, 2 \end{matrix}\middle| {- \frac{e}{4}} \right)} - 2516 \Gamma\left(k + \frac{1}{2}\right)}{8 \left(\gamma - \operatorname{Chi}\left(1\right)\right) \left(k + 1\right) \Gamma\left(k + \frac{1}{2}\right) \Gamma\left(2 k + 3\right)}}$

好久不见，奉上极限：

$\displaystyle{\lim_{k \to \infty}\left(\frac{1258 \sqrt{2} \operatorname{atan}{\left(k \right)} \sqrt{\operatorname{atan}{\left(\frac{\sqrt{2} \pi^{\frac{3}{2}} k}{2516} \right)}}}{\pi^{\frac{3}{2}}}\right)}$

$\displaystyle{\lim_{k \to \infty}\left(\frac{1258 \sqrt{2 \operatorname{atan}{\left(\frac{\sqrt{2} \pi k \sqrt{2 + \pi}}{2516} \right)} + 2} \operatorname{atan}{\left(k \right)}}{\pi \sqrt{2 + \pi}}\right)}$

极限就不能有超大的吗：

$\displaystyle{\lim_{k \to \infty}\left(\frac{\sqrt{6} \left(- \pi^{\frac{5}{3}} \sqrt[3]{- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912} + \pi^{\frac{10}{3}} + \left(- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912\right)^{\frac{2}{3}}\right) \sqrt{\pi^{\frac{2}{3}} \left(6 \operatorname{atan}{\left(\frac{6 \pi^{\frac{2}{3}} k \sqrt[3]{- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912}}{- \pi^{\frac{5}{3}} \sqrt[3]{- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912} + \pi^{\frac{10}{3}} + \left(- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912\right)^{\frac{2}{3}}} \right)} - \pi\right) \sqrt[3]{- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912} + \pi^{\frac{10}{3}} + \left(- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912\right)^{\frac{2}{3}}} \operatorname{atan}{\left(k \right)}}{36 \pi \sqrt{- \pi^{5} + 7548 \sqrt{6} \sqrt{85458456 - \pi^{5}} + 170916912}}\right)}$

$\displaystyle{\lim_{k \to \infty}\left(- \frac{3^{\frac{2}{3}} \left(- \pi^{\frac{3}{2}} \sqrt[6]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} \sqrt{- 30192 \sqrt[3]{3} \pi^{\frac{5}{6}} \left(- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}\right)^{\frac{2}{3}} \sqrt{- 202568192 \cdot 3^{\frac{2}{3}} \pi^{\frac{13}{6}} + 3 \pi^{5} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} + 10064 \sqrt[3]{3} \pi^{\frac{5}{6}} \left(- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}\right)^{\frac{2}{3}}} + 18 \pi^{5} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} \sqrt{- 202568192 \cdot 3^{\frac{2}{3}} \pi^{\frac{13}{6}} + 3 \pi^{5} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} + 10064 \sqrt[3]{3} \pi^{\frac{5}{6}} \left(- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}\right)^{\frac{2}{3}}} + 607704576 \cdot 3^{\frac{2}{3}} \pi^{\frac{13}{6}} \sqrt{- 202568192 \cdot 3^{\frac{2}{3}} \pi^{\frac{13}{6}} + 3 \pi^{5} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} + 10064 \sqrt[3]{3} \pi^{\frac{5}{6}} \left(- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}\right)^{\frac{2}{3}}} + 18 \sqrt{3} \pi^{\frac{15}{2}} \sqrt{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}}} + \sqrt{3} \pi^{\frac{3}{2}} \sqrt[6]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} \left(- 202568192 \cdot 3^{\frac{2}{3}} \pi^{\frac{13}{6}} + 3 \pi^{5} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} + 10064 \sqrt[3]{3} \pi^{\frac{5}{6}} \left(- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}\right)^{\frac{2}{3}}\right)^{\frac{3}{4}} + 3 \pi^{4} \sqrt[3]{- 9 \pi^{\frac{11}{2}} + \sqrt{3} \pi^{2} \sqrt{27 \pi^{7} + 8154585137152}} \sqrt%5 </div>

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