Formula:KLS:09.04:13

{\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x+\textstyle\frac{1}{2% }\mathrm{i};a,b,c,d\right)-p_{n}\!\left(x-\textstyle\frac{1}{2}\mathrm{i};a,b,% c,d\right){}=\mathrm{i}(n+a+b+c+d-1)p_{n-1}\!\left(x;a+\textstyle\frac{1}{2},b% +\textstyle\frac{1}{2},c+\textstyle\frac{1}{2},d+\textstyle\frac{1}{2}\right)}}}

Proof

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