DLMF:14.20.E7 (Q4928): 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: Q11630 / rank
 
Normal rank
Property / Symbols used: Q11630 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q11630 / qualifier
 
xml-id: C14.S1.XMD3.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.m1fdec

Latest revision as of 13:33, 2 January 2020

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DLMF:14.20.E7
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    Statements

    𝖰 ^ - 1 2 + i τ μ ( x ) 1 2 Γ ( μ ) ( 2 1 - x ) μ / 2 , asymptotically-equals Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 1 2 Euler-Gamma 𝜇 superscript 2 1 𝑥 𝜇 2 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{\mu}_{-\frac{1}{2}+i\tau}% \left(x\right)\sim\tfrac{1}{2}\Gamma\left(\mu\right)\left(\frac{2}{1-x}\right)% ^{\mu/2},}}
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    DLMF:14.20.E7
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
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    𝖰 ^ - 1 2 + i τ - μ ( x ) Ferrers-conical-legendre-Q-hat 𝜇 1 2 𝑖 𝜏 𝑥 {\displaystyle{\displaystyle\widehat{\mathsf{Q}}^{-\NVar{\mu}}_{\NVar{-\frac{1% }{2}+i\tau}}\left(\NVar{x}\right)}}
    C14.S20.E2.m2agdec
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    asymptotically-equals {\displaystyle{\displaystyle\sim}}
    C2.S1.E1.m2adec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2amdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1ndec
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    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    C14.S1.XMD3.m1ndec
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    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1fdec
    0 references