DLMF:13.19.E3 (Q4589): Difference between revisions

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Property / constraint
 

| ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{3}{2}\pi-\delta
Property / constraint: | ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}} / rank
 
Normal rank

Revision as of 16:49, 30 December 2019

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DLMF:13.19.E3
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    Statements

    W κ , μ ( z ) e - 1 2 z z κ s = 0 ( 1 2 + μ - κ ) s ( 1 2 - μ - κ ) s s ! ( - z ) - s , asymptotic-expansion Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 superscript subscript 𝑠 0 Pochhammer 1 2 𝜇 𝜅 𝑠 Pochhammer 1 2 𝜇 𝜅 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)\sim e^{-\frac{1}{2}z% }z^{\kappa}\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}{% \left(\frac{1}{2}-\mu-\kappa\right)_{s}}}{s!}{(-z)^{-s}},}}
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    | ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
    0 references