DLMF:5.12.E7 (Q2152)

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DLMF:5.12.E7
No description defined

    Statements

    Defining formula
    ∫ 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),}}
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    DLMF id
    DLMF:5.12.E7
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    constraint
    ℜ ⁡ a > | ℜ ⁡ b | 𝑎 𝑏 {\displaystyle{\displaystyle\Re a>|\Re b|}}
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    Symbols used
    beta function
    Defining formula
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2afdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
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    Q11275
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1fdec
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    Q11283
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1fdec
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