DLMF:31.9.E3 (Q9045): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12492 / rank
 
Normal rank
Property / Symbols used: Q12492 / qualifier
 
Defining formula:

f 0 ⁢ ( q m , z ) subscript 𝑓 0 subscript 𝑞 𝑚 𝑧 {\displaystyle{\displaystyle f_{0}(q_{m},z)}}

f_{0}(q_{m},z)
Property / Symbols used: Q12492 / qualifier
 
xml-id: C31.S9.XMD3.m1dec

Latest revision as of 13:34, 2 January 2020

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DLMF:31.9.E3
No description defined

    Statements

    Defining formula
    θ m = ( 1 - e 2 ⁢ π ⁢ i ⁢ γ ) ⁢ ( 1 - e 2 ⁢ π ⁢ i ⁢ δ ) ⁢ ζ γ ⁢ ( 1 - ζ ) δ ⁢ ( ζ - a ) ϵ ⁢ f 0 ⁢ ( q , ζ ) f 1 ⁢ ( q , ζ ) ⁢ ∂ ∂ ⁡ q ⁡ 𝒲 ⁡ { f 0 ⁢ ( q , ζ ) , f 1 ⁢ ( q , ζ ) } | q = q m , subscript 𝜃 𝑚 evaluated-at 1 2 𝜋 𝑖 𝛾 1 2 𝜋 𝑖 𝛿 superscript 𝜁 𝛾 superscript 1 𝜁 𝛿 superscript 𝜁 𝑎 italic-ϵ subscript 𝑓 0 𝑞 𝜁 subscript 𝑓 1 𝑞 𝜁 partial-derivative 𝑞 Wronskian subscript 𝑓 0 𝑞 𝜁 subscript 𝑓 1 𝑞 𝜁 𝑞 subscript 𝑞 𝑚 {\displaystyle{\displaystyle\theta_{m}=(1-{\mathrm{e}^{2\pi i\gamma}})(1-{% \mathrm{e}^{2\pi i\delta}})\zeta^{\gamma}(1-\zeta)^{\delta}(\zeta-a)^{\epsilon% }\*\frac{f_{0}(q,\zeta)}{f_{1}(q,\zeta)}\left.\frac{\partial}{\partial q}% \mathscr{W}\left\{f_{0}(q,\zeta),f_{1}(q,\zeta)\right\}\right|_{q=q_{m}},}}
    0 references
    DLMF id
    DLMF:31.9.E3
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1bdec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1bdec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1adec
    0 references
    Q12483
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C31.S1.XMD4.m1bdec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1bdec
    0 references
    Q12462
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C31.S1.XMD7.m1adec
    0 references
    Q12491
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C31.S9.XMD1.m1adec
    0 references
    Q12492
    Defining formula
    f 0 ⁢ ( q m , z ) subscript 𝑓 0 subscript 𝑞 𝑚 𝑧 {\displaystyle{\displaystyle f_{0}(q_{m},z)}}
    xml-id
    C31.S9.XMD3.m1dec
    0 references
     
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