Formula:6745

Digital Library of Mathematical Functions ID 18.37.E1

${\displaystyle{\displaystyle R^{(\alpha)}_{m,n}\left(re^{\mathrm{i}\theta}\right)=e^{\mathrm{i}(m-n)\theta}r^{|m-n|}\frac{P^{(\alpha,|m-n|)}_{\min(m,n)}\left(2r^{2}-1\right)}{P^{(\alpha,|m-n|)}_{\min(m,n)}\left(1\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\theta\in\mathbb{R}}}$
${\displaystyle{\displaystyle\theta\in\mathbb{R}}}$
${\displaystyle{\displaystyle\alpha>-1}}$

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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