DLMF:14.7.E19 (Q4771): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11604 / rank
 
Normal rank
Property / Symbols used: Q11604 / qualifier
 
Defining formula:

h {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q11604 / qualifier
 
xml-id: C14.S7.XMD2.m1dec

Latest revision as of 01:31, 2 January 2020

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DLMF:14.7.E19
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    Statements

    n = 0 𝖯 n ( x ) h n = ( 1 - 2 x h + h 2 ) - 1 / 2 , superscript subscript 𝑛 0 shorthand-Ferrers-Legendre-P-first-kind 𝑛 𝑥 superscript 𝑛 superscript 1 2 𝑥 superscript 2 1 2 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\mathsf{P}_{n}\left(x\right)h^{% n}=\left(1-2xh+h^{2}\right)^{-1/2},}}
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    DLMF:14.7.E19
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    𝖯 ν ( x ) = 𝖯 ν 0 ( x ) shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 Ferrers-Legendre-P-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}
    C14.S2.SS2.p2.m2abdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1rdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C14.S1.XMD6.m1pdec
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    h {\displaystyle{\displaystyle h}}
    C14.S7.XMD2.m1dec
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