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Connection between the polylogarithm and the Bernoulli polynomials.

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#complex-analysis #special-functions #zeta-functions #polylogarithm #bernoulli-polynomials
654
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Euler Maclaurin formula proof

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#summation #asymptotics #bernoulli-polynomials
85
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A confusion in Bernoulli equation solution

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#calculus #integration #ordinary-differential-equations #derivatives #bernoulli-polynomials
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Probabilies of rolling n dice to add up to a specific sum

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#probability #bernoulli-polynomials
408
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Series involving Bernoulli Numbers

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#summation #closed-form #bernoulli-numbers #bernoulli-polynomials
120
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quadratic sum of Bernoulli numbers

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#combinatorics #generating-functions #bernoulli-numbers #bernoulli-polynomials
266
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Bernoulli numbers definition as power series

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#complex-analysis #bernoulli-numbers #bernoulli-polynomials
406
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Bernoulli experiment - A coin toss - How to mathematically notate the experiment?

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#probability #statistics #functions #bernoulli-polynomials
146
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How to prove that: $2e^{-2x}(e^x -1)= \displaystyle\sum_{n=1}^\infty \frac{\mu(n)}{\sinh(nx)}$

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#number-theory #analytic-number-theory #bernoulli-polynomials
261
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Integral of product of two Bernoulli polynomials

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#definite-integrals #bernoulli-polynomials
8.4k
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Sum of powers of natural numbers

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#summation #bernoulli-polynomials
456
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How to get the explicit formula of Bernoulli polynomial using its generating function?

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#functional-analysis #generating-functions #bernoulli-polynomials
91
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Convergence of a sequence which is built with Bernoulli polynomials

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#calculus #convergence-divergence #analytic-number-theory #bernoulli-numbers #bernoulli-polynomials
122
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Is it obvious intuitively that $1^p + 2^p + \cdots (n-1)^p$ is a polynomial in $n$?

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#intuition #bernoulli-numbers #bernoulli-polynomials
151
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Question in Ch-12 Apostol's Number theory (Vol1)

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#number-theory #analytic-number-theory #bernoulli-polynomials

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