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Post Closed as "Not suitable for this site" by Nate Eldredge, Chris Godsil, Michael Renardy, Stefan Waldmann, Alexandre Eremenko
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Nate Eldredge
Nate Eldredge
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system of Laguerre polynomials is orthonormal basis in space $L_2((0, \infty),e^tdte^{-t}dt)$

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Gera Slanova
Gera Slanova
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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^tdt)$$L_2((0, \infty),e^{-t}dt)$ ?

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 $L_2((0, \infty),e^tdt)$ ?

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 $L_2((0, \infty),e^{-t}dt)$ ?

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Gera Slanova
Gera Slanova
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system of Laguerre polynomials is orthonormal basis in space $L_2((0, \infty),e^tdt)$

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 $L_2((0, \infty),e^tdt)$ ?