Formula:KLS:09.04:25: Difference between revisions

From DRMF
Jump to navigation Jump to search
imported>SeedBot
DRMF
 
m Move page script moved page Formula:KLS:09.04:25 to F:KLS:09.04:25
 
(No difference)

Latest revision as of 08:34, 22 December 2019


lim t → ∞ ⁡ p n ⁡ ( x ⁢ t ; 1 2 ⁢ ( - N + i ⁢ ν - 2 ⁢ t ) , 1 2 ⁢ ( - N - i ⁢ ν + 2 ⁢ t ) , 1 2 ⁢ ( - N + i ⁢ ν - 2 ⁢ t ) , 1 2 ( - N - i ν + 2 t ) ) t n = ( n - 2 ⁢ N - 1 ) n n ! ⁢ P n ⁡ ( x ; ν , N ) subscript → 𝑡 fragments continuous-Hahn-polynomial 𝑛 𝑥 𝑡 1 2 𝑁 imaginary-unit 𝜈 2 𝑡 1 2 𝑁 imaginary-unit 𝜈 2 𝑡 1 2 𝑁 imaginary-unit 𝜈 2 𝑡 fragments 1 2 fragments ( N imaginary-unit ν 2 t ) superscript 𝑡 𝑛 Pochhammer-symbol 𝑛 2 𝑁 1 𝑛 𝑛 pseudo-Jacobi-polynomial 𝑛 𝑥 𝜈 𝑁 {\displaystyle{\displaystyle{\displaystyle\lim_{t\rightarrow\infty}\frac{p_{n}% \!\left(xt;\frac{1}{2}(-N+\mathrm{i}\nu-2t),\frac{1}{2}(-N-\mathrm{i}\nu+2t),% \frac{1}{2}(-N+\mathrm{i}\nu-2t),\frac{1}{2}(-N-\mathrm{i}\nu+2t\right))}{t^{n% }}{}=\frac{{\left(n-2N-1\right)_{n}}}{n!}P_{n}\!\left(x;\nu,N\right)}}}

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

p n subscript 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}  : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
i i {\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}  : imaginary unit : http://dlmf.nist.gov/1.9.i
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
P n subscript 𝑃 𝑛 {\displaystyle{\displaystyle{\displaystyle P_{n}}}}  : pseudo Jacobi polynomomal : http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi

Bibliography

Equation in Section 9.4 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:09.04:25&oldid=3473"