DLMF:14.18.E6 (Q4907): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(One intermediate revision by the same user not shown)
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.m3abdec
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.m1adec

Latest revision as of 12:28, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.18.E6
No description defined

    Statements

    test
    ( x - y ) ⁢ ∑ k = 0 n ( 2 ⁢ k + 1 ) ⁢ P k ⁡ ( x ) ⁢ P k ⁡ ( y ) = ( n + 1 ) ⁢ ( P n + 1 ⁡ ( x ) ⁢ P n ⁡ ( y ) - P n ⁡ ( x ) ⁢ P n + 1 ⁡ ( y ) ) , 𝑥 𝑦 superscript subscript 𝑘 0 𝑛 2 𝑘 1 shorthand-Legendre-P-first-kind 𝑘 𝑥 shorthand-Legendre-P-first-kind 𝑘 𝑦 𝑛 1 shorthand-Legendre-P-first-kind 𝑛 1 𝑥 shorthand-Legendre-P-first-kind 𝑛 𝑦 shorthand-Legendre-P-first-kind 𝑛 𝑥 shorthand-Legendre-P-first-kind 𝑛 1 𝑦 {\displaystyle{\displaystyle(x-y)\sum_{k=0}^{n}(2k+1)P_{k}\left(x\right)P_{k}% \left(y\right)=(n+1)\left(P_{n+1}\left(x\right)P_{n}\left(y\right)-P_{n}\left(% x\right)P_{n+1}\left(y\right)\right),}}
    0 references
    DLMF id
    DLMF:14.18.E6
    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.m3abdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q4907&oldid=27646"