DLMF:13.24.E3 (Q4651): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11588 / rank
 
Normal rank
Property / Symbols used: Q11588 / qualifier
 
Defining formula:

p s subscript 𝑝 𝑠 {\displaystyle{\displaystyle p_{s}}}

p_{s}
Property / Symbols used: Q11588 / qualifier
 
xml-id: C13.S24.XMD1.m1adec

Latest revision as of 01:05, 2 January 2020

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DLMF:13.24.E3
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    Statements

    Defining formula
    exp ⁡ ( - 1 2 ⁢ z ⁢ ( coth ⁡ t - 1 t ) ) ⁢ ( t sinh ⁡ t ) 1 - 2 ⁢ μ = ∑ s = 0 ∞ p s ( μ ) ⁢ ( z ) ⁢ ( - t z ) s . 1 2 𝑧 hyperbolic-cotangent 𝑡 1 𝑡 superscript 𝑡 𝑡 1 2 𝜇 superscript subscript 𝑠 0 superscript subscript 𝑝 𝑠 𝜇 𝑧 superscript 𝑡 𝑧 𝑠 {\displaystyle{\displaystyle\exp\left(-\tfrac{1}{2}z\left(\coth t-\frac{1}{t}% \right)\right)\left(\frac{t}{\sinh t}\right)^{1-2\mu}=\sum_{s=0}^{\infty}p_{s}% ^{(\mu)}(z)\left(-\frac{t}{z}\right)^{s}.}}
    0 references
    DLMF id
    DLMF:13.24.E3
    0 references
    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    hyperbolic cotangent function
    Defining formula
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
    Q11558
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C13.S1.XMD3.m1bdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1bdec
    0 references
    Q11588
    Defining formula
    p s subscript 𝑝 𝑠 {\displaystyle{\displaystyle p_{s}}}
    xml-id
    C13.S24.XMD1.m1adec
    0 references
     
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