If Hn (x) is the nth order Hermite polynomial, then which of the following integrals is equal to 0? O sº H; (x) H, (x) e¯ª dx -00 O ° H; (x) H2 (x) e-2ª dæ -00 O s° H; (x) H2 (x) dx -00 O ° H; (x) H2 (x) e¬¤¨ dæ -00
If Hn (x) is the nth order Hermite polynomial, then which of the following integrals is equal to 0? O sº H; (x) H, (x) e¯ª dx -00 O ° H; (x) H2 (x) e-2ª dæ -00 O s° H; (x) H2 (x) dx -00 O ° H; (x) H2 (x) e¬¤¨ dæ -00
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Transcribed Image Text:If \( H_n(x) \) is the nth order Hermite polynomial, then which of the following integrals is equal to 0?
- \(\circ \quad \int_{-\infty}^{\infty} H_5(x) H_2(x) e^{-x} \, dx\)
- \(\circ \quad \int_{-\infty}^{\infty} H_5(x) H_2(x) e^{-2x} \, dx\)
- \(\circ \quad \int_{-\infty}^{\infty} H_5(x) H_2(x) \, dx\)
- \(\circ \quad \int_{-\infty}^{\infty} H_5(x) H_2(x) e^{-x^2} \, dx\)
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