Orthogonality of Laguerre L
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Theorem
The following formula holds: $$\displaystyle\int_0^{\infty} e^{-x} L_n(x) L_m(x) \mathrm{d}x = \delta_{mn},$$ where $e^{-x}$ denotes the exponential, $L_n$ denotes Laguerre L, and $\delta$ denotes Kronecker delta.
Proof
References
- 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.4
