Formula:6604

Digital Library of Mathematical Functions ID 18.23.E7

${\displaystyle{\displaystyle(1-e^{\mathrm{i}\phi}z)^{-\lambda+\mathrm{i}x}(1-e^{-\mathrm{i}\phi}z)^{-\lambda-\mathrm{i}x}=\sum_{n=0}^{\infty}P^{(\lambda)}_{n}\left(x;\phi\right)z^{n},}}$

Constraint(s)

${\displaystyle{\displaystyle|z|<1}}$

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};\NVar{\phi}\right)}}$: Meixner–Pollaczek polynomial
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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