DLMF:5.12.E7 (Q2152): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 18:44, 1 January 2020

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DLMF:5.12.E7
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    Statements

    test
    ∫ 0 ∞ cosh ⁡ ( 2 ⁢ b ⁢ t ) ( cosh ⁡ t ) 2 ⁢ a ⁢ d t = 4 a - 1 ⁢ B ⁡ ( a + b , a - b ) , superscript subscript 0 2 𝑏 𝑡 superscript 𝑡 2 𝑎 𝑡 superscript 4 𝑎 1 Euler-Beta 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\cosh\left(2bt\right)}{(% \cosh t)^{2a}}\mathrm{d}t=4^{a-1}\mathrm{B}\left(a+b,a-b\right),}}
    0 references
    DLMF id
    DLMF:5.12.E7
    0 references
    constraint
    ℜ ⁡ a > | ℜ ⁡ b | 𝑎 𝑏 {\displaystyle{\displaystyle\Re a>|\Re b|}}
    0 references
    Symbols used
    beta function
    test
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2afdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
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