# Question about parabolic cylinder functions

1. Jan 26, 2013

### PRB147

In table of integrals, series and products 7ed. by Gradshtyn and Ryzhik,
in page 1028, there is an expression:
$$D_p(z)=\int_{-\infty}^{\infty}x^p e^{-2x^2+2i xz}dx,~~(Re~ p>-1; ~for~ x<0, ~arg x^p=p\pi i)$$

what is the meaning of $$for~ x<0, ~arg x^p=p\pi i)$$

Last edited: Jan 26, 2013
2. Jan 26, 2013

### tiny-tim

Hi PRB147!
if x is negative, then x = |x|e±πi

so xp could be defined as either |x|pepπi or |x|pe-pπi

the question is merely telling you to adopt the former definition!

3. Jan 30, 2013

### PRB147

thank you, tiny-tim!
I remember that arg(z) is a real number.