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variants of this functions
Factorial






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Factorial[n] > Summation > Infinite summation > Parameter-containing sums





http://functions.wolfram.com/06.01.23.0047.01









  


  










Input Form





Sum[k!^3/(k + 2 n)!^3, {k, 0, Infinity}] == Sum[((-1)^j (35 + 8 (-11 + 7 n - 7 j) (n - j)) (-1 + n)!^2 n! (-2 + 6 n)! (3 n - 3 j)! (-1 + 2 n - 2 j)!^6)/(16 (1 - 2 n + 2 j)^6 (-1 + n - j)^5 (3 n)! (-1 + 2 n)!^6 (-3 + 2 n - 2 j)!^3 (-2 + 6 n - 6 j)! (-1 + n - j)!^2 (n - j)!), {j, 0, n - 2}] + (((-1)^(-1 + n) (-1 + n)!^2 n! (-2 + 6 n)!) (10 - Pi^2))/ (4 (3 n)! (-1 + 2 n)!^6) /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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<apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Contributed by





Troy Kessler










Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.