DLMF:13.24.E2 (Q4650): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
test:

J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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.m2aadec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11558 / rank
 
Normal rank
Property / Symbols used: Q11558 / qualifier
 
test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q11558 / qualifier
 
xml-id: C13.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11588 / rank
 
Normal rank
Property / Symbols used: Q11588 / qualifier
 
test:

p s subscript 𝑝 𝑠 {\displaystyle{\displaystyle p_{s}}}

p_{s}
Property / Symbols used: Q11588 / qualifier
 
xml-id: C13.S24.XMD1.m1dec

Latest revision as of 00:05, 2 January 2020

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DLMF:13.24.E2
No description defined

    Statements

    test
    1 Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ M κ , μ ⁡ ( z ) = 2 2 ⁢ μ ⁢ z μ + 1 2 ⁢ ∑ s = 0 ∞ p s ( μ ) ⁢ ( z ) ⁢ ( 2 ⁢ κ ⁢ z ) - 2 ⁢ μ - s ⁢ J 2 ⁢ μ + s ⁡ ( 2 ⁢ κ ⁢ z ) , 1 Euler-Gamma 1 2 𝜇 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 superscript 2 2 𝜇 superscript 𝑧 𝜇 1 2 superscript subscript 𝑠 0 superscript subscript 𝑝 𝑠 𝜇 𝑧 superscript 2 𝜅 𝑧 2 𝜇 𝑠 Bessel-J 2 𝜇 𝑠 2 𝜅 𝑧 {\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}% \left(z\right)=2^{2\mu}z^{\mu+\frac{1}{2}}\sum_{s=0}^{\infty}p_{s}^{(\mu)}(z)% \left(2\sqrt{\kappa z}\right)^{-2\mu-s}J_{2\mu+s}\left(2\sqrt{\kappa z}\right)% ,}}
    0 references
    DLMF id
    DLMF:13.24.E2
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    test
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2aadec
    0 references
    Q11558
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C13.S1.XMD3.m1adec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1adec
    0 references
    Q11588
    test
    p s subscript 𝑝 𝑠 {\displaystyle{\displaystyle p_{s}}}
    xml-id
    C13.S24.XMD1.m1dec
    0 references
     
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