C n^(lambda)'(x)=2lambda C (n+1)^(lambda+1)(x)

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Theorem

The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} C_n^{\lambda}(x)=2\lambda C_{n+1}^{\lambda+1}(x),$$ where $C_n^{\lambda}$ denotes Gegenbauer C.

Proof

References