Is this inequality true?

  • Thread starter eljose
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  • #1
eljose
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let be the inequality:

[tex][\frac{\Gamma(1/4-b/2-it/2)}{\Gamma(1/4+b/2+it/2)}]<\frac{\Gamma(1/4-b/2)}{\Gamma(1/4+b/2)} [/tex]

where [] means modulus of the complex number...
 

Answers and Replies

  • #2
matt grime
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and gamma is the gamma function presumably... is b any real or complex number? and t? apparently b must be real, looking at it. i mean, is the rhs modded too?
 
  • #3
eljose
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b and t are both real and [tex]\Gamma(x)=\int_0^{\infty}t^{x-1}e^{-t}dt [/tex]
 
Last edited:
  • #4
shmoe
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It's certainly not true for any b, remember the asymptotic I gave you for [tex]\chi[/tex] before? It can easily tell you which b's even have a chance for this to be true and also that for these b's it will hold for a large enough |t| (though not uniformly).
 

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