DLMF:14.18.E7 (Q4908): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11447 / rank
 
Normal rank
Property / Symbols used: Q11447 / qualifier
 
test:

P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}

\assLegendreP[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreP[0]{\nu}@{z}
Property / Symbols used: Q11447 / qualifier
 
xml-id: C14.S2.SS2.p2.m3acdec
Property / Symbols used
 
Property / Symbols used: Q11448 / rank
 
Normal rank
Property / Symbols used: Q11448 / qualifier
 
test:

Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}

\assLegendreQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreQ[0]{\nu}@{z}
Property / Symbols used: Q11448 / qualifier
 
xml-id: C14.S2.SS2.p2.m5aadec
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.m1bdec

Latest revision as of 12:28, 2 January 2020

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DLMF:14.18.E7
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    Statements

    test
    ( x - y ) ⁢ ∑ k = 0 n ( 2 ⁢ k + 1 ) ⁢ P k ⁡ ( x ) ⁢ Q k ⁡ ( y ) = ( n + 1 ) ⁢ ( P n + 1 ⁡ ( x ) ⁢ Q n ⁡ ( y ) - P n ⁡ ( x ) ⁢ Q n + 1 ⁡ ( y ) ) - 1 . 𝑥 𝑦 superscript subscript 𝑘 0 𝑛 2 𝑘 1 shorthand-Legendre-P-first-kind 𝑘 𝑥 shorthand-Legendre-Q-second-kind 𝑘 𝑦 𝑛 1 shorthand-Legendre-P-first-kind 𝑛 1 𝑥 shorthand-Legendre-Q-second-kind 𝑛 𝑦 shorthand-Legendre-P-first-kind 𝑛 𝑥 shorthand-Legendre-Q-second-kind 𝑛 1 𝑦 1 {\displaystyle{\displaystyle(x-y)\sum_{k=0}^{n}(2k+1)P_{k}\left(x\right)Q_{k}% \left(y\right)=(n+1)\left(P_{n+1}\left(x\right)Q_{n}\left(y\right)-P_{n}\left(% x\right)Q_{n+1}\left(y\right)\right)-1.}}
    0 references
    DLMF id
    DLMF:14.18.E7
    0 references
    Symbols used
    Q11447
    test
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3acdec
    0 references
    Q11448
    test
    Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m5aadec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1bdec
    0 references
     
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