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Question about parabolic cylinder functions

  1. Jan 26, 2013 #1
    In table of integrals, series and products 7ed. by Gradshtyn and Ryzhik,
    in page 1028, there is an expression:
    [tex]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)[/tex]

    what is the meaning of [tex]for~ x<0, ~arg x^p=p\pi i)[/tex]
    Last edited: Jan 26, 2013
  2. jcsd
  3. Jan 26, 2013 #2


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    Hi PRB147! :smile:
    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! :wink:
  4. Jan 30, 2013 #3
    thank you, tiny-tim!
    I remember that arg(z) is a real number.
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