Formula:KLS:09.03:14

<< Formula:KLS:09.03:10

formula in Continuous dual Hahn

Formula:KLS:09.03:15 >>

${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left((x+\textstyle\frac{1}{2}\mathrm{i})^{2};a,b,c\right)-S_{n}\!\left((x-\textstyle\frac{1}{2}\mathrm{i})^{2};a,b,c\right){}=-2\mathrm{i}nxS_{n-1}\!\left(x^{2};a+\textstyle\frac{1}{2},b+\textstyle\frac{1}{2},c+\textstyle\frac{1}{2}\right)}}}$

Proof

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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

Bibliography

Equation in Section 9.3 of KLS.

URL links

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formula in Continuous dual Hahn

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