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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/06.01.23.0045.01









  


  










Input Form





Sum[k!^3/(k + 2 n + 1)!^3, {k, 0, Infinity}] == ((3 n)!/(n!^3 (2 n)!^3)) Sum[((-1)^j (5 - 32 n + 56 n^2 + 32 j - 112 n j + 56 j^2) (-1 + n - j)!^3)/(4 (-1 + 2 n - 2 j)^2 (3 n - 3 j)!), {j, 0, n - 1}] + (((-1)^n (3 n)!) Zeta[3])/(n!^3 (2 n)!^3) /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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Contributed by





Troy Kessler










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





2007-05-02





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