No output from integrating complicated function

Questions
1

Hi all,
Could you please help me how to solve this integration.

B = L* Exp[-L*y]* Gamma[1 + m, 0, Sqrt[g (y + h)/(p (1 - (v^2 + u^2)*g))]/n] / Gamma[1 + m]

A = Integrate[B, {y, 0, Infinity}]

Integ.png
Integ.png643×223 9.21 KB

2

You have the Gamma (with a capital G) function twice in your code, but in the image it is a lower case gamma. What is lower case gamma?

If you mean for gamma to be the incomplete Gamma function, then the closed form doesn’t exist. However, with a suitable scaling, it is fairly easy to find numerical values for the integral:

Plot[With[{m = q}, 
  NIntegrate[Exp[-y] Gamma[1 + m, 0, Sqrt[y]], {y, 0, Infinity}]], {q,
   0, 10}]

Note: this question is a repost of this stackexchange which also has comments.

3

Hi Carter,

The lower case gamma denotes the lower incomplete gamma function while the one with the upper case denotes the complete gamma function.