DLMF:14.11.E1 (Q4817): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q11605 / rank
 
Normal rank
Property / Symbols used: Q11605 / qualifier
 
Defining formula:

𝖠 ν μ ⁢ ( x ) superscript subscript 𝖠 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\mathsf{A}_{\nu}^{\mu}(x)}}

\mathsf{A}_{\nu}^{\mu}(x)
Property / Symbols used: Q11605 / qualifier
 
xml-id: C14.S11.XMD1.m1dec

Latest revision as of 01:40, 2 January 2020

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DLMF:14.11.E1
No description defined

    Statements

    Defining formula
    ∂ ∂ ⁡ ν ⁡ 𝖯 ν μ ⁡ ( x ) = π ⁢ cot ⁡ ( ν ⁢ π ) ⁢ 𝖯 ν μ ⁡ ( x ) - 1 π ⁢ 𝖠 ν μ ⁢ ( x ) , partial-derivative 𝜈 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜋 𝜈 𝜋 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 1 𝜋 superscript subscript 𝖠 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\frac{\partial}{\partial\nu}\mathsf{P}^{\mu}_{\nu}% \left(x\right)=\pi\cot\left(\nu\pi\right)\mathsf{P}^{\mu}_{\nu}\left(x\right)-% \frac{1}{\pi}\mathsf{A}_{\nu}^{\mu}(x),}}
    0 references
    DLMF id
    DLMF:14.11.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2adec
    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
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.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
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
    0 references
    Q11605
    Defining formula
    𝖠 ν μ ⁢ ( x ) superscript subscript 𝖠 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\mathsf{A}_{\nu}^{\mu}(x)}}
    xml-id
    C14.S11.XMD1.m1dec
    0 references
     
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