3 Mellin transforms

  • Thread starter eljose
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let,s suppose we have the equality:

f(x)g(x)=H(x) now we have that f(x) and H(x) have no Mellin transform..then would be fair to do this?..

[tex]f(x)=\frac{1}{2i\pi}\int_{c-i\infty}^{c+i\infty}t^{-s}\frac{M[H(x)]}{M[g(x)]}ds[/tex]
 
Last edited:
493
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Another question..does the Mellin transform of [tex]ln\zeta(as)[/tex] exist? where a >0 and real

and the transform of some of derivatives of [tex]ln\zeta(as)[/tex] ?
 
Last edited:
493
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another question let be the integral:

[tex]M(s)=\int_0^{\infty}f(t)t^{s-1} [/tex] then we take the derivative respecto to s

[tex]dM(s)/ds=\int_0^{\infty}ln(t)f(t)t^{s-1} [/tex] so then if dM(s)/ds=r(s) then:

[tex]M(s)=\int_s^{\infty}r(p)dp [/tex] is that correct?..thanx
 

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