Unusual finding in the deriving of the Gamma function

Forum|Forum|9 years ago
September 24, 2016
6 replies
3427 views

Hello,

In the derivation of the Gamma function, in its integral representation, you get an unusual result shown in the figure in the green rectangle. What to do to not generate it?

The result is correct, but the fact that Mathcad, in representing the generalized integral with the limit, has changed the variable of integration, assigning any, in the example X253, surprises me somewhat.

Gamma derivative.jpg

Thanks for the attention

With best regards

Calculus_Derivatives

Best answer by LucMeekes

Here's Mathcad 11 (Maple engine):

Success!

Luc

24-Ruby IV

Author

21-Topaz II

Thanks V. O. Me too Mathcad produces the same result. But I was interested in the derivation of the integral representation.

Greetings

A

AlvaroDíaz

12-Amethyst

Hi F.M.

Well, first, mupad isn't very good doing integrals, the value for your problem can be founded here: Wolfram|Alpha: Integral‌

Mupad introduces a "bound variable" because of the manipulations inside the integral for the calculus of the derivative, probably for ensure that this bound variable don't change for some reason in the process.

You can see an old discussion about bound variables (where I call them as "mute variables") at integral of azimuthal angle for the probe current . For me, the best practice is never use the same variable name inside the integral and the integral limits, as I defend in that post, but Tom Gutman disagree about that.