Can you help me to prove that system of Laguerre polynomials $$ L_n = \dfrac{e^t}{n!}\dfrac{d^n}{dt^n} (t^n e^{-t})$$ is orthonormal basis in space $L_2((0, \infty),e^{-t}dt)$ ?
system of Laguerre polynomials is orthonormal basis in space $L_2((0, \infty),e^{-t}dt)$
Gera Slanova
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