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How to deduce the result $\zeta(2k)_{k\to \infty} \to 1$

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#number-theory #analytic-number-theory #bernoulli-numbers
373
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Bernoulli number generating function proof problem

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#combinatorics #discrete-mathematics #generating-functions #fake-proofs #bernoulli-numbers
39
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Probability of a voting majority given people changing their votes (Bernouilli trials)

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#bernoulli-numbers
128
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Computing residue involving Bernoulli numbers

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#complex-analysis #residue-calculus #bernoulli-numbers
49
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Does $\sum_{n=0}^{\infty}\frac{B_{n-1}}{n!}B_n(z)$ have closed form?

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#calculus #bernoulli-numbers #bernoulli-polynomials
173
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Bernoulli numbers and a reference in Gamma function chapter

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#complex-analysis #residue-calculus #laurent-series #bernoulli-numbers
67
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Decomposition of $\psi^{(n)}(1)$ in terms of $\psi^{(n)}(k)$

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#reference-request #special-functions #bernoulli-numbers #polygamma
121
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Are the Bernoulli numbers $B_{2n}$ given by an elementary function of $n$?

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#factorial #elementary-functions #bernoulli-numbers #bernoulli-polynomials
312
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Delta method for asymptotic variance

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#poisson-distribution #variance #bernoulli-numbers #delta-method
69
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Why is $\sum_{n=1}^\infty (-1)^n\frac{\zeta(2n)}{\pi^{2n}} = \frac{1}{1-e^2}$?

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#sequences-and-series #riemann-zeta #bernoulli-numbers
34
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problem understanding proof for bernouli numbers generating function

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#calculus #bernoulli-numbers
333
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Sum $\sum_{(k_1, k_2, k_3): k_1+k_2+k_3=K, \,\, n_1+n_2+n_3=N}k_1^{n_1}\times k_2^{n_2} \times k_3^{n_3}$

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#combinatorics #number-theory #elementary-number-theory #bernoulli-numbers #bernoulli-polynomials
452
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How to use Euler-Maclaurin summation to show the following relationship over Gamma function

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#gamma-function #binomial-theorem #bernoulli-numbers #euler-maclaurin
538
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Faulhaber's polynomials and irreducibility in the sums of powers

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#sequences-and-series #irreducible-polynomials #bernoulli-numbers
99
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Another sum involving Benoulli numbers

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#sequences-and-series #bernoulli-numbers

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