DLMF:10.21.E17 (Q3301): Difference between revisions

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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 15:42, 2 January 2020

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DLMF:10.21.E17
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    Statements

    Defining formula
    d c d ν = 2 ⁢ c ⁢ ∫ 0 ∞ K 0 ⁡ ( 2 ⁢ c ⁢ sinh ⁡ t ) ⁢ e - 2 ⁢ ν ⁢ t ⁢ d t , derivative 𝑐 𝜈 2 𝑐 superscript subscript 0 modified-Bessel-second-kind 0 2 𝑐 𝑡 superscript 𝑒 2 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle\frac{\mathrm{d}c}{\mathrm{d}\nu}=2c\int_{0}^{% \infty}K_{0}\left(2c\sinh t\right)e^{-2\nu t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.21.E17
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    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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