Formula:6714

Digital Library of Mathematical Functions ID 18.33.E11

${\displaystyle{\displaystyle z^{-n+1}\phi_{2n-1}(z)={C_{n}p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)+D_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)},}}$

Symbols List

• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\phi_{n}(z)}}$: polynomials
• ${\displaystyle{\displaystyle q_{n}(x)}}$: an orthogonal polynomial
• ${\displaystyle{\displaystyle p_{n}(x)}}$: an orthogonal polynomial
• ${\displaystyle{\displaystyle C_{n}}}$: coefficient
• ${\displaystyle{\displaystyle D_{n}}}$: coefficient
 

Resources that cite this formula

No records found.