Unusual finding in the deriving of the Gamma function

[-MFra-]

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.

Thanks for the attention

With best regards

[ValeryOchkov]

[-MFra-]

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

Greetings

[AlvaroDíaz]

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.

F.M. wrote:

What to do to not generate it?

I don't see an easy way. Here my atemps.

Best regards.

Alvaro.

[-MFra-]

Hello,

to think of it, Mathcad solves the problem in its own way, and let the user will choose the variable of integration that he desires.

I remain waiting for some more comments from other users.

Thank you

Best regards

FM

[LucMeekes · Accepted solution]

Here's Mathcad 11 (Maple engine):

Success!

Luc

[ValeryOchkov]

Maple 2016