Ramanujan's Master Theorem

Author

Eric W. Weisstein
October 21, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegralTransforms/RamanujansMasterTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RamanujansMasterTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

ϕ(n) = 1

Sum[1(-x)^k/k!,{k,0,∞}]

Integrate[x^(n-1)Exp[-x],{x,0,∞},Assumptions->n>0]

ϕ(n) = n

Sum[k(-x)^k/k!,{k,0,∞}]

Integrate[-x^(n-1)x Exp[-x],{x,0,∞}]

FunctionExpand[-n Gamma[n]]