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Question Number 8517 by Chantria last updated on 14/Oct/16

Commented by prakash jain last updated on 14/Oct/16

$$n+\mathrm{ve}\mathrm{integer}?$$

Commented by Yozzias last updated on 15/Oct/16

$$\mathrm{I}=\ln \left[\frac{1}{\sqrt{2\pi }}{2}^{\mathrm{n}}{\mathrm{e}}^{-\mathrm{nq}/2}\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}{\mathrm{e}}^{-{\mathrm{u}}^2}{\cosh }^{\mathrm{n}}(\sqrt{\mathrm{q}}\mathrm{u}+\mathrm{m})\mathrm{du}\right]$$$$\mathrm{I}=\ln \left[\frac{1}{\sqrt{2\pi }}{2}^{\mathrm{n}+1}{\mathrm{e}}^{-\mathrm{nq}/2}\underset{0}{\stackrel{\mathrm{\infty }}{\int }}{\mathrm{e}}^{-{\mathrm{u}}^2}{\cosh }^{\mathrm{n}}(\sqrt{\mathrm{q}}\mathrm{u}+\mathrm{m})\mathrm{du}\right]$$$$$$

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