DLMF:14.8.E3 (Q4777): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11596 / rank
 
Normal rank
Property / Symbols used: Q11596 / qualifier
 
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)}}

\FerrersQ[]{\NVar{\nu}}@{\NVar{x}}=\FerrersQ[0]{\nu}@{x}
Property / Symbols used: Q11596 / qualifier
 
xml-id: C14.S2.SS2.p2.m4adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1bdec

Latest revision as of 01:32, 2 January 2020

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DLMF:14.8.E3
No description defined

    Statements

    Defining formula
    𝖰 ν ⁡ ( x ) = 1 2 ⁢ ln ⁡ ( 2 1 - x ) - γ - ψ ⁡ ( ν + 1 ) + O ⁡ ( 1 - x ) , shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 1 2 2 1 𝑥 digamma 𝜈 1 Big-O 1 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\nu}\left(x\right)=\frac{1}{2}\ln\left% (\frac{2}{1-x}\right)-\gamma-\psi\left(\nu+1\right)+O\left(1-x\right),}}
    0 references
    DLMF id
    DLMF:14.8.E3
    0 references
    constraint
    ν ≠ - 1 , - 2 , - 3 , … 𝜈 1 2 3 … {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    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.m4adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1bdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1bdec
    0 references
     
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