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Formula:747

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Digital Library of Mathematical Functions ID 2.5.E1

ℳ ⁡ f ⁡ ( z ) = ∫ 0 ∞ t z - 1 ⁢ f ⁢ ( t ) ⁢ d t , Mellin-transform 𝑓 𝑧 superscript subscript 0 superscript 𝑡 𝑧 1 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(z% \right)=\int_{0}^{\infty}t^{z-1}f(t)\mathrm{d}t,}}


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
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}} : locally integrable function
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This page was last edited on 3 March 2024, at 01:36.
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