DLMF:24.7.E9 (Q7485): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
Defining formula:

cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

\cosh@@{\NVar{z}}
Property / Symbols used: hyperbolic cosine function / qualifier
 
xml-id: C4.S28.E2.m2abdec

Revision as of 01:35, 2 January 2020

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DLMF:24.7.E9
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    Statements

    Defining formula
    E 2 ⁢ n ⁡ ( x ) = ( - 1 ) n ⁢ 4 ⁢ ∫ 0 ∞ sin ⁡ ( π ⁢ x ) ⁢ cosh ⁡ ( π ⁢ t ) cosh ⁡ ( 2 ⁢ π ⁢ t ) - cos ⁡ ( 2 ⁢ π ⁢ x ) ⁢ t 2 ⁢ n ⁢ d t , Euler-polynomial-E 2 𝑛 𝑥 superscript 1 𝑛 4 superscript subscript 0 𝜋 𝑥 𝜋 𝑡 2 𝜋 𝑡 2 𝜋 𝑥 superscript 𝑡 2 𝑛 𝑡 {\displaystyle{\displaystyle E_{2n}\left(x\right)=(-1)^{n}4\int_{0}^{\infty}% \frac{\sin\left(\pi x\right)\cosh\left(\pi t\right)}{\cosh\left(2\pi t\right)-% \cos\left(2\pi x\right)}t^{2n}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:24.7.E9
    0 references
    Symbols used
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2abdec
    0 references
     
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