Questions tagged [euler-mascheroni-constant]

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What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?

I am a first year graduate student and I am eager to work on irrationality/transcendental proofs of specific numbers like Euler's constant gamma. Because backgrounds for Elliptic Curves include very ...
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Ergodic Theory and Euler-Mascheroni Constant

I am highly interested in doing research on proving irrationality of some specific numbers like Euler-Mascheroni Constant or $\zeta(5)$. A professor guided me that arithmetic nature of constants are a ...
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Beta function, harmonic numbers, and integral values

A problem of Mathematical Physics that I am working on involves the computation of a certain integral. Part of the result reads: $$ I_k:= [\beta_x( -1 - k, 0) + H_{-2 - k}]x^k $$ where $\beta_x( -1 - ...
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Construction, similar to Chow's EL-numbers? Is it valid? What are the properties?

The idea of EL-numbers, proposed by Chow, impressed me very much, so I decided to build something similar and look what this will turn out. Instead of $\exp(x)$ and $\ln(x)$ functions as the building ...
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A set of divergent integrals that I think, equal to $-\gamma$

So, we take $\frac{\text{sgn}(x-1)}{x}$ and apply $\mathcal{L}_t[t f(t)](x)$ four times. The transform is known to keep area under the curve. These integrals, I think, are equal to minus Euler-...
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