Formula:6597

Digital Library of Mathematical Functions ID 18.22.E30

${\displaystyle{\displaystyle\delta_{x}\left(w^{(\lambda+\frac{1}{2})}(x;\phi)P^{(\lambda+\frac{1}{2})}_{n}\left(x;\phi\right)\right)=-(n+1)w^{(\lambda)}(x;\phi)P^{(\lambda)}_{n+1}\left(x;\phi\right).}}$

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x};\NVar{\phi}\right)}}$: Meixner–Pollaczek polynomial
• ${\displaystyle{\displaystyle\delta_{\NVar{x}}}}$: central difference
• ${\displaystyle{\displaystyle w(x)}}$: weight function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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