Formula:KLS:09.08:01

From DRMF
Revision as of 00:34, 6 March 2017 by imported>SeedBot (DRMF)
Jump to navigation Jump to search


C n λ ⁡ ( x ) = ( 2 ⁢ λ ) n ( λ + 1 2 ) n ⁢ P n ( λ - 1 2 , λ - 1 2 ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 Pochhammer-symbol 2 𝜆 𝑛 Pochhammer-symbol 𝜆 1 2 𝑛 Jacobi-polynomial-P 𝜆 1 2 𝜆 1 2 𝑛 𝑥 {\displaystyle{\displaystyle{\displaystyle C^{\lambda}_{n}\left(x\right)=\frac% {{\left(2\lambda\right)_{n}}}{{\left(\lambda+\frac{1}{2}\right)_{n}}}P^{(% \lambda-\frac{1}{2},\lambda-\frac{1}{2})}_{n}\left(x\right)}}}

Constraint(s)

λ ≠ 0 𝜆 0 {\displaystyle{\displaystyle{\displaystyle\lambda\neq 0}}}


Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

C n μ subscript superscript 𝐶 𝜇 𝑛 {\displaystyle{\displaystyle{\displaystyle C^{\mu}_{n}}}}  : ultraspherical/Gegenbauer polynomial : http://dlmf.nist.gov/18.3#T1.t1.r5
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
P n ( α , β ) subscript superscript 𝑃 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}}}}  : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

Bibliography

Equation in Section 9.8 of KLS.

URL links

We ask users to provide relevant URL links in this space.


Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Formula:KLS:09.08:01&oldid=1663"