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3 questions with no upvoted or accepted answers
6
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431
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How to prove these identities for $\log(2)$ based on $_3F_2$ integrals?
In this MO post I have placed 4 Ramanujan-type hypergeometric series found using the LLL algorithm for fast computing of some logarithms. I could prove 3 of them by means of classical methods based on ...
- 2,836
2
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249
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Calculating $\int_1^{\infty}\frac{\operatorname{ali}(x)}{x^3}dx$, where $\operatorname{ali}(x)$ is the inverse function of the logarithmic integral
It is well-known that we can compute the closed-form of the integrals $$\int_1^{\infty}\frac{\log x}{x^2}dx$$
and $$\int_1^{\infty}\frac{\operatorname{li} (x)}{x^3}dx,$$
where $\operatorname{li} (x)$ ...
2
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0
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114
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Is there an explicit version of Morse Lemma used in stationary phase method?
In the proof of the stationary phase method (at least the one I have seen) Morse lemma shows up, which states: Let $g:\mathbb R^n\to \mathbb R$ be a function of class $C^\infty$ for which $0$ is a ...
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