DLMF:14.8.E15 (Q4789): Difference between revisions

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

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2akdec
Property / Symbols used
 
Property / Symbols used: Q11592 / rank
 
Normal rank
Property / Symbols used: Q11592 / qualifier
 
Defining formula:

𝑸 ν μ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}

\assLegendreOlverQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11592 / qualifier
 
xml-id: C14.S21.SS1.p1.m3aadec
Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
Defining formula:

asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2akdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aedec
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.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1idec
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.m1ldec

Latest revision as of 01:34, 2 January 2020

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DLMF:14.8.E15
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    Statements

    𝑸 ν μ ( x ) π 1 / 2 Γ ( ν + 3 2 ) ( 2 x ) ν + 1 , asymptotically-equals associated-Legendre-black-Q 𝜇 𝜈 𝑥 superscript 𝜋 1 2 Euler-Gamma 𝜈 3 2 superscript 2 𝑥 𝜈 1 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)\sim\frac{% \pi^{1/2}}{\Gamma\left(\nu+\frac{3}{2}\right)(2x)^{\nu+1}},}}
    0 references
    DLMF:14.8.E15
    0 references
    ν - 3 2 , - 5 2 , - 7 2 , 𝜈 3 2 5 2 7 2 {\displaystyle{\displaystyle\nu\neq-\tfrac{3}{2},-\tfrac{5}{2},-\tfrac{7}{2},% \dots}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2akdec
    0 references
    𝑸 ν μ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    C14.S21.SS1.p1.m3aadec
    0 references
    asymptotically-equals {\displaystyle{\displaystyle\sim}}
    C2.S1.E1.m2akdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1ndec
    0 references
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1idec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1ldec
    0 references