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141
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Borel summation of a divergent series as the best estimate of a function

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#asymptotics #power-series #divergent-series #formal-power-series #summation-method
30
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What if $b$ is an even integer in Weierstrass function?

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#analysis #derivatives #convergence-divergence #divergent-series
64
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Identify a number series

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#sequences-and-series #divergent-series
235
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Derive a formula $\sum_{j=1}^{n-1}j^a \sim \zeta(-a)+\frac{n^{a+1}}{a+1}\sum_{s=0}^\infty \binom{a+1}{s}\frac{B_s}{n^s} $

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#integration #sequences-and-series #summation #asymptotics #divergent-series
149
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$\cos 2\pi n\theta> 1-\varepsilon$ infinitely often?

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#real-analysis #reference-request #divergent-series
142
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Is there any intuition of why the both, regularized logarithm of zero is $-\gamma$ and the regularized logarithm of Bernoulli umbra is $-\gamma$?

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#intuition #divergent-series #euler-mascheroni-constant #big-picture #umbral-calculus
201
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Why does the harmonic series diverge?

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#sequences-and-series #convergence-divergence #divergent-series
113
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The Cauchy-product of these divergent, infinite series converges

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#sequences-and-series #divergent-series #cauchy-product
73
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When do log-series go laurent and why?

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#taylor-expansion #laurent-series #divergent-series
71
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Rationale for validity of the binomial expansion involving rational powers

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#binomial-theorem #divergent-series
184
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Puiseux vs Taylor series expansion

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#taylor-expansion #power-series #divergent-series
55
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Expansion of divergent function with Legendre polynomials

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#sequences-and-series #divergent-series #legendre-polynomials
290
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Generalized $p$-Series and a Related Series

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#real-analysis #sequences-and-series #divergent-series
50
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Proving series is divergent by definition

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#real-analysis #sequences-and-series #divergent-series
160
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Sum of infinite series of fractions with powers of 2 in denominators

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#sequences-and-series #arithmetic #divergent-series

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