Formula:757

Digital Library of Mathematical Functions ID 2.5.E11

${\displaystyle{\displaystyle\Residue_{z=n}\left[x^{-z}\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}\mskip-3.0mu h\mskip 3.0mu \left(z\right)\right]=(a_{n}\ln x+b_{n})x^{-n},}}$

Symbols List

• ${\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}\right)}}$: Mellin transform
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Residue}}$:
• ${\displaystyle{\displaystyle h(t)={J_{\nu}^{2}}\left(t\right)}}$: function
• ${\displaystyle{\displaystyle a_{n}}}$: coefficients
• ${\displaystyle{\displaystyle b_{n}}}$: coefficients
• ${\displaystyle{\displaystyle f(t)=1/(1+t)}}$: function
 

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