DLMF:11.10.E4 (Q4021): Difference between revisions

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

sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2adec

Revision as of 14:54, 2 January 2020

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DLMF:11.10.E4
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    Statements

    Defining formula
    𝐀 ν ⁡ ( z ) = 1 π ⁢ ∫ 0 ∞ e - ν ⁢ t - z ⁢ sinh ⁡ t ⁢ d t , associated-Anger-Weber-A 𝜈 𝑧 1 𝜋 superscript subscript 0 superscript 𝑒 𝜈 𝑡 𝑧 𝑡 𝑡 {\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
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    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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