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I have the following input

m = 2;
Gamma[n + m]/Gamma[n + 1];
FullSimplify[%]

It gives me

1+n

For m=3, it gives me

(1 + n) (2 + n)

For m=4, it gives me

(1 + n) (2 + n) (3 + n)

For m=5, it gives me

Gamma[5 + n]/Gamma[1 + n]

I would like to have expression like (1 + n) (2 + n) (3 + n) (4+n), how should I do to get it?

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1 Answer 1

4
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You can use FunctionExpand for this.

gammaFRatio[m_] := FunctionExpand[Gamma[n + m]/Gamma[n + 1]]

Example:

gammaFRatio[10]
(1 + n) (2 + n) (3 + n) (4 + n) (5 + n) (6 + n) (7 + n) (8 + n) (9 + n)
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