DLMF:11.10.E4 (Q4021)

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DLMF:11.10.E4
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    Statements

    Defining formula
    𝐀 Ξ½ ⁑ ( z ) = 1 Ο€ ⁒ ∫ 0 ∞ e - Ξ½ ⁒ t - z ⁒ sinh ⁑ t ⁒ d t , associated-Anger-Weber-A 𝜈 𝑧 1 πœ‹ superscript subscript 0 superscript 𝑒 𝜈 𝑑 𝑧 𝑑 𝑑 {\displaystyle{\displaystyle\mathbf{A}_{\nu}\left(z\right)=\frac{1}{\pi}\int_{% 0}^{\infty}e^{-\nu t-z\sinh t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:11.10.E4
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    constraint
    β„œ ⁑ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    Ο€ {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x π‘₯ {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    hyperbolic sine function
    Defining formula
    sinh ⁑ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
     
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