DLMF:14.7.E20 (Q4772): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11604 / rank
 
Normal rank
Property / Symbols used: Q11604 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q11604 / qualifier
 
xml-id: C14.S7.XMD2.m1adec

Latest revision as of 01:31, 2 January 2020

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DLMF:14.7.E20
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    Statements

    Defining formula
    ∑ n = 0 ∞ 𝖰 n ⁡ ( x ) ⁢ h n = 1 ( 1 - 2 ⁢ x ⁢ h + h 2 ) 1 / 2 ⁢ ln ⁡ ( x - h + ( 1 - 2 ⁢ x ⁢ h + h 2 ) 1 / 2 ( 1 - x 2 ) 1 / 2 ) . superscript subscript 𝑛 0 shorthand-Ferrers-Legendre-Q-first-kind 𝑛 𝑥 superscript ℎ 𝑛 1 superscript 1 2 𝑥 ℎ superscript ℎ 2 1 2 𝑥 ℎ superscript 1 2 𝑥 ℎ superscript ℎ 2 1 2 superscript 1 superscript 𝑥 2 1 2 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\mathsf{Q}_{n}\left(x\right)h^{% n}=\frac{1}{\left(1-2xh+h^{2}\right)^{1/2}}\*\ln\left(\frac{x-h+\left(1-2xh+h^% {2}\right)^{1/2}}{\left(1-x^{2}\right)^{1/2}}\right).}}
    0 references
    DLMF id
    DLMF:14.7.E20
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11596
    Defining formula
    𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m4abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1sdec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1qdec
    0 references
    Q11604
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C14.S7.XMD2.m1adec
    0 references
     
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