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closed form of the following integral :$\int_{0}^{\infty}- \sqrt{x}+ \sqrt{x}\coth (x) dx$?

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#integration #definite-integrals #closed-form #gamma-function #zeta-functions
123
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Simplify convoluted $\text{prime}^*$ numbers sum formulae

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#prime-numbers #zeta-functions #pseudoprimes
2.1k
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Binomial expansion with gamma function

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#riemann-zeta #zeta-functions
227
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Trace and Det of Laplacian on the rectangle

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#eigenvalues-eigenvectors #determinant #trace #laplacian #zeta-functions
99
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The isomorphism of $\mathbb{Z}_{p}[x] /\left(x^{n}-1\right)$ using Hensel's Lemma

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#abstract-algebra #algebraic-geometry #riemann-zeta #p-adic-number-theory #zeta-functions
133
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The limit $\lim_{s\to 1}\left(\zeta_K(s)-\frac{\pi}{4(s-1)}\right)$.

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#number-theory #algebraic-number-theory #zeta-functions
40
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Zeta function of the hypersurface of some homogeneous polynomial

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#number-theory #analytic-number-theory #analytic-functions #zeta-functions
54
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About the non-trivial zeros of the Riemann zeta function.

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#analysis #zeta-functions
364
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Analytic Continuation of Mellin Transforms and the Prime Zeta Function

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#complex-analysis #zeta-functions #mellin-transform
120
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Asymptotic expansion of $Li^{-1}$ and zeros of $F(s)$ and $G(s)$

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#asymptotics #analytic-number-theory #visualization #zeta-functions #analytic-continuation
51
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Apparent link between the zeta function and $\ln(10)$

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#zeta-functions
163
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How to write $\zeta(s)^3$ as a function of the generalized Mobius function?

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#zeta-functions #mobius-function #mobius-inversion
171
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Why the Riemann Zeta function has nontrivial zeros

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#number-theory #roots #zeta-functions #riemann-hypothesis
321
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Are any values of this sum involving the Thue Morse sequence known?

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#sequences-and-series #zeta-functions
103
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Is Lerch's transcendent a multi-valued function?

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#complex-analysis #special-functions #zeta-functions

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