DLMF:18.30.E6 (Q6004): Difference between revisions

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Property / constraint
 

n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}

n=0,1,\dots
Property / constraint: n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: associated Jacobi polynomial / rank
 
Normal rank
Property / Symbols used: associated Jacobi polynomial / qualifier
 
Defining formula:

P n ( α , β ) ⁡ ( x ; c ) associated-Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑐 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x};\NVar{c}\right)}}

\assJacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}{\NVar{c}}
Property / Symbols used: associated Jacobi polynomial / qualifier
 
xml-id: C18.S30.E4.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11790 / rank
 
Normal rank
Property / Symbols used: Q11790 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11790 / qualifier
 
xml-id: C18.S30.XMD1.m1ddec

Latest revision as of 13:26, 2 January 2020

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DLMF:18.30.E6
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    Statements

    Defining formula
    P n ⁡ ( x ; c ) = P n ( 0 , 0 ) ⁡ ( x ; c ) , Legendre-spherical-polynomial-P 𝑛 𝑥 𝑐 associated-Jacobi-polynomial-P 0 0 𝑛 𝑥 𝑐 {\displaystyle{\displaystyle P_{n}\left(x;c\right)=P^{(0,0)}_{n}\left(x;c% \right),}}
    0 references
    DLMF id
    DLMF:18.30.E6
    0 references
    constraint
    n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}
    0 references
    Symbols used
    associated Jacobi polynomial
    Defining formula
    P n ( α , β ) ⁡ ( x ; c ) associated-Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑐 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x};\NVar{c}\right)}}
    xml-id
    C18.S30.E4.m2abdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references
    Q11790
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S30.XMD1.m1ddec
    0 references
     
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