DLMF:14.7.E16 (Q4768): 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.m1addec
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.m1odec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1mdec

Latest revision as of 00:30, 2 January 2020

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English
DLMF:14.7.E16
No description defined

    Statements

    test
    𝖯 n m ⁡ ( x ) = P n m ⁡ ( x ) = 0 , Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 Legendre-P-first-kind 𝑚 𝑛 𝑥 0 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)=P^{m}_{n}\left(x% \right)=0,}}
    0 references
    DLMF id
    DLMF:14.7.E16
    0 references
    constraint
    m > n 𝑚 𝑛 {\displaystyle{\displaystyle m>n}}
    0 references
    Symbols used
    Ferrers function of the first kind
    test
    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.m2acdec
    0 references
    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.m1addec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1odec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1gdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1mdec
    0 references
     
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