# Questions tagged [euler-mascheroni-constant]

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Let $p_n$ be the $n$th degree polynomial that sends $\frac{k(k-1)}{2}$ to $\frac{k(k+1)}{2}$ for $k=1,2,...,n+1$. E.g., $p_2(x) = (6+13x -x^2)/6$ is the unique quadratic polynomial $p(x)$ satisfying $... 1 vote 0 answers 129 views ### An identity among values of the logarithmic derivative of$\zeta(s)$From some known special values of the Riemann zeta function and its derivative, one can show that $$\gamma =1+ \frac{\zeta'(2)}{\zeta(2)} -\frac{\zeta'(0)}{\zeta(0)}+ \frac{\zeta'(-1)}{\zeta(-1)}.$$ ... 3 votes 0 answers 342 views ### Extending reals with logarithm of zero: properties and reference request If we take logarithmic function, we can see that its real part at zero approaches negative infinity with the same rate and sign from any direction on the complex plane, while the Cauchy main value of ... 0 votes 0 answers 137 views ### 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 ... 1 vote 0 answers 215 views ### 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 ... 4 votes 1 answer 425 views ### 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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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 ...
### 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-...