DLMF:29.8.E5 (Q8709): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
Defining formula:

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1abdec

Revision as of 01:22, 2 January 2020

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DLMF:29.8.E5
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    Statements

    Defining formula
    𝐸𝑐 ν 2 ⁢ m ⁡ ( z 1 , k 2 ) ⁢ w 2 ⁢ ( K ⁡ ) - w 2 ⁢ ( - K ⁡ ) d w 2 ⁢ ( z ) / d z | z = 0 = ∫ - K ⁡ K ⁡ 𝖯 ν ⁡ ( y ) ⁢ 𝐸𝑐 ν 2 ⁢ m ⁡ ( z , k 2 ) ⁢ d z , Lame-Ec 2 𝑚 𝜈 subscript 𝑧 1 superscript 𝑘 2 subscript 𝑤 2 complete-elliptic-integral-first-kind-K 𝑘 subscript 𝑤 2 complete-elliptic-integral-first-kind-K 𝑘 evaluated-at derivative subscript 𝑤 2 𝑧 𝑧 𝑧 0 superscript subscript complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-first-kind-K 𝑘 shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑦 Lame-Ec 2 𝑚 𝜈 𝑧 superscript 𝑘 2 𝑧 {\displaystyle{\displaystyle\mathit{Ec}^{2m}_{\nu}\left(z_{1},k^{2}\right)% \frac{w_{2}(K)-w_{2}(-K)}{\left.\ifrac{\mathrm{d}w_{2}(z)}{\mathrm{d}z}\right|% _{z=0}}=\int_{-K}^{K}\mathsf{P}_{\nu}\left(y\right)\mathit{Ec}^{2m}_{\nu}\left% (z,k^{2}\right)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:29.8.E5
    0 references
    Symbols used
    Q12362
    Defining formula
    𝐸𝑐 ν m ⁡ ( z , k 2 ) Lame-Ec 𝑚 𝜈 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{Ec}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S3.SS4.p1.m5adec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1abdec
    0 references
     
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