Formula:KLS:09.08:77: Difference between revisions

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T n ⁡ ( x ) := P n ( - 1 2 , - 1 2 ) ⁡ ( x ) P n ( - 1 2 , - 1 2 ) ⁡ ( 1 ) assign Chebyshev-polynomial-first-kind-T 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 Jacobi-polynomial-P 1 2 1 2 𝑛 1 {\displaystyle{\displaystyle{\displaystyle T_{n}\left(x\right):=\frac{P^{(-% \frac{1}{2},-\frac{1}{2})}_{n}\left(x\right)}{P^{(-\frac{1}{2},-\frac{1}{2})}_% {n}\left(1\right)}}}}

Proof

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Symbols List

T n subscript 𝑇 𝑛 {\displaystyle{\displaystyle{\displaystyle T_{n}}}}  : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8
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

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