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Formula:757

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Digital Library of Mathematical Functions ID 2.5.E11

res z = n ⁡ [ x - z ⁢ ℳ ⁡ f ⁡ ( 1 - z ) ⁢ ℳ ⁡ h ⁡ ( z ) ] = ( a n ⁢ ln ⁡ x + b n ) ⁢ x - n , subscript residue 𝑧 𝑛 delimited-[] superscript 𝑥 𝑧 Mellin-transform 𝑓 1 𝑧 Mellin-transform ℎ 𝑧 subscript 𝑎 𝑛 𝑥 subscript 𝑏 𝑛 superscript 𝑥 𝑛 {\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},}}


Constraint(s)

Symbols List

  • ℳ ⁡ ( f ) ⁡ ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}} : Mellin transform
  • ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}} : principal branch of logarithm function
  • res residue {\displaystyle{\displaystyle\Residue}} :
  • h ⁢ ( t ) = J ν 2 ⁡ ( t ) ℎ 𝑡 Bessel-J 𝜈 2 𝑡 {\displaystyle{\displaystyle h(t)={J_{\nu}^{2}}\left(t\right)}} : function
  • a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}} : coefficients
  • b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}} : coefficients
  • f ⁢ ( t ) = 1 / ( 1 + t ) 𝑓 𝑡 1 1 𝑡 {\displaystyle{\displaystyle f(t)=1/(1+t)}} : function
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:02.
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