Formula:KLS:09.03:17

<< Formula:KLS:09.03:16

formula in Continuous dual Hahn

Formula:KLS:09.03:19 >>

${\displaystyle{\displaystyle{\displaystyle\frac{\delta\left[\omega(x;a,b,c)S_{n}\!\left(x^{2};a,b,c\right)\right]}{\delta x^{2}}{}=\omega(x;a-\textstyle\frac{1}{2},b-\textstyle\frac{1}{2},c-\textstyle\frac{1}{2})S_{n+1}\!\left(x^{2};a-\textstyle\frac{1}{2},b-\textstyle\frac{1}{2},c-\textstyle\frac{1}{2}\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle\omega(x;a,b,c)=\frac{1}{2\mathrm{i}x}\left|\frac{\Gamma\left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)\Gamma\left(c+\mathrm{i}x\right)}{\Gamma\left(2\mathrm{i}x\right)}\right|^{2}}}}$

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

${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 9.3 of KLS.

URL links

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

<< Formula:KLS:09.03:16

formula in Continuous dual Hahn

Formula:KLS:09.03:19 >>