Formula:6742

Digital Library of Mathematical Functions ID 18.35.E7

${\displaystyle{\displaystyle(1-ze^{\mathrm{i}\theta})^{-\lambda+\mathrm{i}\tau_{a,b}(\theta)}(1-ze^{-\mathrm{i}\theta})^{-\lambda-\mathrm{i}\tau_{a,b}(\theta)}=\sum_{n=0}^{\infty}P^{(\lambda)}_{n}\left(\cos\theta;a,b\right)z^{n},}}$

Constraint(s)

${\displaystyle{\displaystyle 0<\theta<\pi}}$

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b}\right)}}$: Pollaczek polynomial
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\tau_{a,b}(\theta)}}$: 18.35.E3
 

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