DLMF:15.9.E19 (Q5109): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11481 / rank
 
Normal rank
Property / Symbols used: Q11481 / qualifier
 
test:

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11481 / qualifier
 
xml-id: C14.S21.SS1.p1.m1acdec

Revision as of 13:11, 2 January 2020

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DLMF:15.9.E19
No description defined

    Statements

    test
    𝐅 ⁡ ( a , b a - b + 1 ; z ) = z ( b - a ) / 2 ⁢ ( 1 - z ) - b ⁢ P - b b - a ⁡ ( 1 + z 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑎 𝑏 1 𝑧 superscript 𝑧 𝑏 𝑎 2 superscript 1 𝑧 𝑏 Legendre-P-first-kind 𝑏 𝑎 𝑏 1 𝑧 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a-b+1};z\right)=z^{% \ifrac{(b-a)}{2}}(1-z)^{-b}\*P^{b-a}_{-b}\left(\frac{1+z}{1-z}\right),}}
    0 references
    DLMF id
    DLMF:15.9.E19
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}
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    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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    Symbols used
    Q11481
    test
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1acdec
    0 references
     
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