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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/06.01.23.0043.01









  


  








Input Form





Sum[k!^4/(k + n)!^4, {k, 0, Infinity}] == Subscript[a, n] /; Element[n, Integers] && n > 0 && Subscript[a, 1] == Pi^4/90 && Subscript[a, 2] == (1/45) (-1575 + 150 Pi^2 + Pi^4) && (Subscript[a, n] == (1/((-2 + n)^3 (-1 + n)^7)) (4 (-1 + 4 (-2 + n)) (1 + 4 (-2 + n)) a[-2 + n] + 2 (1 + 2 (-2 + n)) (1 + 3 (-2 + n) + 3 (-2 + n)^2) (-2 + n)^3 Subscript[a, n - 1] - (5 (2 + 10 (-2 + n) + 15 (-2 + n)^2) (-2 + n) (-1 + n)^3)/(-1 + n)!^4) /; n > 2)








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