# Integral involving power , exp and exp(power)

1. Feb 4, 2012

### yfatehi

I need some help evaluating the following integral from 0 to inifinity and a,p,c are positive reals, p>=1

\int\limit_0^\infty\ x^{p-1}e^{-x}e^{-c x^a} dx

2. Feb 4, 2012

### mathman

In general it can be done only numerically - probably using a series expansion of e-cxa.

3. Feb 5, 2012

### yfatehi

How can use the series expansion

4. Feb 5, 2012

### mathman

After the expansion each term will be e-x times a power of x. If the powers are integers, then explicit term by term integration is possible. If they are not integers, I can't see anything but brute force numerical integration

5. Feb 12, 2012

### yfatehi

If I have a power series is the variable x which is uniformaly absolutely convergent over the entire positive Reals domain and then I multipled this series by F(x) which does not depend on the series index n. ie all the series terms are multipiled by the same fuction. Will the resulting series preserve the convergence properties?

6. Feb 12, 2012

### mathman

It will as long as |F(x)G(x)| is integrable, where G(x) is the function represented by the power series.

7. Feb 13, 2012