DLMF:1.14.E34 (Q495): Difference between revisions

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Revision as of 23:36, 19 December 2021

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DLMF:1.14.E34
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    DLMF defining formula
    1 2 ⁢ ( f ⁢ ( u + ) + f ⁢ ( u - ) ) = 1 2 ⁢ π ⁢ i ⁢ lim T → ∞ ⁡ ∫ σ - i ⁢ T σ + i ⁢ T u - s ⁢ ℳ ⁡ f ⁡ ( s ) ⁢ d s . 1 2 𝑓 limit-from 𝑢 𝑓 limit-from 𝑢 1 2 𝜋 𝑖 subscript → 𝑇 subscript superscript 𝜎 𝑖 𝑇 𝜎 𝑖 𝑇 superscript 𝑢 𝑠 Mellin-transform 𝑓 𝑠 𝑠 {\displaystyle{\displaystyle\tfrac{1}{2}(f(u+)+f(u-))=\frac{1}{2\pi i}\lim_{T% \to\infty}\int^{\sigma+iT}_{\sigma-iT}u^{-s}\mathscr{M}\mskip-3.0mu f\mskip 3.% 0mu \left(s\right)\mathrm{d}s.}}
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