Formula:KLS:09.08:44

From DRMF
Revision as of 08:35, 22 December 2019 by Move page script (talk | contribs) (Move page script moved page Formula:KLS:09.08:44 to F:KLS:09.08:44)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search


R n ( α , β ) ⁡ ( x ) := P n ( α , β ) ⁡ ( x ) / P n ( α , β ) ⁡ ( 1 ) ⁢ ω n ( α , β ) := ∫ - 1 1 ( 1 - x ) α ⁢ ( 1 + x ) β ⁢ 𝑑 x ∫ - 1 1 ( R n ( α , β ) ⁡ ( x ) ) 2 ⁢ ( 1 - x ) α ⁢ ( 1 + x ) β ⁢ 𝑑 x assign normalized-Jacobi-polynomial-R 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 superscript subscript 𝜔 𝑛 𝛼 𝛽 assign superscript subscript 1 1 superscript 1 𝑥 𝛼 superscript 1 𝑥 𝛽 differential-d 𝑥 superscript subscript 1 1 superscript normalized-Jacobi-polynomial-R 𝛼 𝛽 𝑛 𝑥 2 superscript 1 𝑥 𝛼 superscript 1 𝑥 𝛽 differential-d 𝑥 {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}\left(x\right% ):=P^{(\alpha,\beta)}_{n}\left(x\right)/P^{(\alpha,\beta)}_{n}\left(1\right)% \omega_{n}^{(\alpha,\beta)}:=\frac{\int_{-1}^{1}(1-x)^{\alpha}(1+x)^{\beta}dx}% {\int_{-1}^{1}(R^{(\alpha,\beta)}_{n}\left(x\right))^{2}(1-x)^{\alpha}(1+x)^{% \beta}dx}}}}

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

R n ( α , β ) subscript superscript 𝑅 𝛼 𝛽 𝑛 {\displaystyle{\displaystyle{\displaystyle R^{(\alpha,\beta)}_{n}}}}  : normalized Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:normJacobiR
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
∫ {\displaystyle{\displaystyle{\displaystyle\int}}}  : integral : http://dlmf.nist.gov/1.4#iv

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:09.08:44&oldid=3717"