Formula:KLS:09.03:08: Difference between revisions

From DRMF
Jump to navigation Jump to search
imported>SeedBot
DRMF
 
m Move page script moved page Formula:KLS:09.03:08 to F:KLS:09.03:08
 
(No difference)

Latest revision as of 08:34, 22 December 2019


x ⁢ S ^ n ⁡ ( x ) = S ^ n + 1 ⁡ ( x ) + ( A n + C n - a 2 ) ⁢ S ^ n ⁡ ( x ) + A n - 1 ⁢ C n ⁢ S ^ n - 1 ⁡ ( x ) 𝑥 continuous-dual-Hahn-monic-p 𝑛 𝑥 𝑎 𝑏 𝑐 continuous-dual-Hahn-monic-p 𝑛 1 𝑥 𝑎 𝑏 𝑐 subscript 𝐴 𝑛 subscript 𝐶 𝑛 superscript 𝑎 2 continuous-dual-Hahn-monic-p 𝑛 𝑥 𝑎 𝑏 𝑐 subscript 𝐴 𝑛 1 subscript 𝐶 𝑛 continuous-dual-Hahn-monic-p 𝑛 1 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle{\displaystyle x{\widehat{S}}_{n}\!\left(x\right)=% {\widehat{S}}_{n+1}\!\left(x\right)+(A_{n}+C_{n}-a^{2}){\widehat{S}}_{n}\!% \left(x\right)+A_{n-1}C_{n}{\widehat{S}}_{n-1}\!\left(x\right)}}}

Substitution(s)

C n = n ⁢ ( n + b + c - 1 ) subscript 𝐶 𝑛 𝑛 𝑛 𝑏 𝑐 1 {\displaystyle{\displaystyle{\displaystyle C_{n}=n(n+b+c-1)}}} &
A n = ( n + a + b ) ⁢ ( n + a + c ) subscript 𝐴 𝑛 𝑛 𝑎 𝑏 𝑛 𝑎 𝑐 {\displaystyle{\displaystyle{\displaystyle A_{n}=(n+a+b)(n+a+c)}}}


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

& : logical and
S ^ n subscript ^ 𝑆 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{S}}_{n}}}}  : monic continuous dual Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsdualHahn

Bibliography

Equation in Section 9.3 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:09.03:08&oldid=3401"