DLMF:18.35.E7 (Q6046): Difference between revisions

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Property / constraint
 

0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}

0<\theta<\pi
Property / constraint: 0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}} / rank
 
Normal rank

Revision as of 17:04, 30 December 2019

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DLMF:18.35.E7
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    ( 1 - z e i θ ) - λ + i τ a , b ( θ ) ( 1 - z e - i θ ) - λ - i τ a , b ( θ ) = n = 0 P n ( λ ) ( cos θ ; a , b ) z n , superscript 1 𝑧 superscript 𝑒 imaginary-unit 𝜃 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 superscript 1 𝑧 superscript 𝑒 imaginary-unit 𝜃 𝜆 imaginary-unit subscript 𝜏 𝑎 𝑏 𝜃 superscript subscript 𝑛 0 Pollaczek-polynomial-P 𝜆 𝑛 𝜃 𝑎 𝑏 superscript 𝑧 𝑛 {\displaystyle{\displaystyle(1-ze^{\mathrm{i}\theta})^{-\lambda+\mathrm{i}\tau% _{a,b}(\theta)}(1-ze^{-\mathrm{i}\theta})^{-\lambda-\mathrm{i}\tau_{a,b}(% \theta)}=\sum_{n=0}^{\infty}P^{(\lambda)}_{n}\left(\cos\theta;a,b\right)z^{n},}}
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    0 < θ < π 0 𝜃 𝜋 {\displaystyle{\displaystyle 0<\theta<\pi}}
    0 references