DLMF:2.4.E15 (Q769): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2acdec

Revision as of 15:59, 1 January 2020

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DLMF:2.4.E15
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    a b e - z p ( t ) q ( t ) d t 2 e - z p ( t 0 ) s = 0 Γ ( s + 1 2 ) b 2 s z s + ( 1 / 2 ) , asymptotic-expansion superscript subscript 𝑎 𝑏 superscript 𝑒 𝑧 𝑝 𝑡 𝑞 𝑡 𝑡 2 superscript 𝑒 𝑧 𝑝 subscript 𝑡 0 superscript subscript 𝑠 0 Euler-Gamma 𝑠 1 2 subscript 𝑏 2 𝑠 superscript 𝑧 𝑠 1 2 {\displaystyle{\displaystyle\int_{a}^{b}e^{-zp(t)}q(t)\mathrm{d}t\sim 2e^{-zp(% t_{0})}\sum_{s=0}^{\infty}\Gamma\left(s+\tfrac{1}{2}\right)\frac{b_{2s}}{z^{s+% (1/2)}},}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
    0 references