DLMF:13.24.E1 (Q4649): Difference between revisions

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2 μ , κ + μ - 1 , - 2 , - 3 , formulae-sequence 2 𝜇 𝜅 𝜇 1 2 3 {\displaystyle{\displaystyle 2\mu,\kappa+\mu\neq-1,-2,-3,\dots}}

2\mu,\kappa+\mu\neq-1,-2,-3,\dots
Property / constraint: 2 μ , κ + μ - 1 , - 2 , - 3 , formulae-sequence 2 𝜇 𝜅 𝜇 1 2 3 {\displaystyle{\displaystyle 2\mu,\kappa+\mu\neq-1,-2,-3,\dots}} / rank
 
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Revision as of 17:50, 30 December 2019

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DLMF:13.24.E1
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    M κ , μ ( z ) = Γ ( κ + μ ) 2 2 κ + 2 μ z 1 2 - κ s = 0 ( - 1 ) s ( 2 κ + 2 μ ) s ( 2 κ ) s ( 1 + 2 μ ) s s ! ( κ + μ + s ) I κ + μ + s ( 1 2 z ) , Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Euler-Gamma 𝜅 𝜇 superscript 2 2 𝜅 2 𝜇 superscript 𝑧 1 2 𝜅 superscript subscript 𝑠 0 superscript 1 𝑠 Pochhammer 2 𝜅 2 𝜇 𝑠 Pochhammer 2 𝜅 𝑠 Pochhammer 1 2 𝜇 𝑠 𝑠 𝜅 𝜇 𝑠 modified-Bessel-first-kind 𝜅 𝜇 𝑠 1 2 𝑧 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)=\Gamma\left(\kappa+% \mu\right)2^{2\kappa+2\mu}z^{\frac{1}{2}-\kappa}\*\sum_{s=0}^{\infty}(-1)^{s}% \frac{{\left(2\kappa+2\mu\right)_{s}}{\left(2\kappa\right)_{s}}}{{\left(1+2\mu% \right)_{s}}s!}\*\left(\kappa+\mu+s\right)I_{\kappa+\mu+s}\left(\tfrac{1}{2}z% \right),}}
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    DLMF:13.24.E1
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    2 μ , κ + μ - 1 , - 2 , - 3 , formulae-sequence 2 𝜇 𝜅 𝜇 1 2 3 {\displaystyle{\displaystyle 2\mu,\kappa+\mu\neq-1,-2,-3,\dots}}
    0 references