Orthogonality of Laguerre L

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.

References

• 1968: W.W. Bell: Special Functions for Scientists and Engineers ... (previous) ... (next): Theorem 6.4