DLMF:14.14.E3 (Q4844): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11470 / rank
 
Normal rank
Property / Symbols used: Q11470 / qualifier
 
test:

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

\assLegendreQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11470 / qualifier
 
xml-id: C14.S21.SS1.p1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11608 / rank
 
Normal rank
Property / Symbols used: Q11608 / qualifier
 
test:

x k subscript 𝑥 𝑘 {\displaystyle{\displaystyle x_{k}}}

x_{k}
Property / Symbols used: Q11608 / qualifier
 
xml-id: C14.S14.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11609 / rank
 
Normal rank
Property / Symbols used: Q11609 / qualifier
 
test:

x k subscript 𝑥 𝑘 {\displaystyle{\displaystyle x_{k}}}

x_{k}
Property / Symbols used: Q11609 / qualifier
 
xml-id: C14.S14.XMD2.m1bdec

Latest revision as of 00:46, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.14.E3
No description defined

    Statements

    test
    ( ν - μ ) ⁢ Q ν μ ⁡ ( x ) Q ν - 1 μ ⁡ ( x ) = x 0 y 0 - x 1 y 1 - x 2 y 2 - ⋯ , 𝜈 𝜇 Legendre-Q-second-kind 𝜇 𝜈 𝑥 Legendre-Q-second-kind 𝜇 𝜈 1 𝑥 continued-fraction subscript 𝑥 0 subscript 𝑦 0 continued-fraction subscript 𝑥 1 subscript 𝑦 1 continued-fraction subscript 𝑥 2 subscript 𝑦 2 ⋯ {\displaystyle{\displaystyle(\nu-\mu)\frac{Q^{\mu}_{\nu}\left(x\right)}{Q^{\mu% }_{\nu-1}\left(x\right)}=\cfrac{x_{0}}{y_{0}-\cfrac{x_{1}}{y_{1}-\cfrac{x_{2}}% {y_{2}-\cdots}}},}}
    0 references
    DLMF id
    DLMF:14.14.E3
    0 references
    constraint
    ν ≠ μ 𝜈 𝜇 {\displaystyle{\displaystyle\nu\neq\mu}}
    0 references
    Symbols used
    Q11470
    test
    Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m2adec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references
    Q11591
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1bdec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1bdec
    0 references
    Q11608
    test
    x k subscript 𝑥 𝑘 {\displaystyle{\displaystyle x_{k}}}
    xml-id
    C14.S14.XMD1.m1bdec
    0 references
    Q11609
    test
    x k subscript 𝑥 𝑘 {\displaystyle{\displaystyle x_{k}}}
    xml-id
    C14.S14.XMD2.m1bdec
    0 references
     
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