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On determining the constant term in Stirling's approximation

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#asymptotics #factorial #gamma-function #euler-maclaurin
2.3k
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Taylor series of $e^{-1/x}$

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#integration #taylor-expansion #improper-integrals #euler-lagrange-equation #euler-maclaurin
45
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How was this simplification done?

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#power-series #binomial-coefficients #binomial-theorem #negative-binomial #euler-maclaurin
47
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How to taylor expand $1/(1- \frac{k}{r})$ where k is some constant

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#taylor-expansion #binomial-theorem #negative-binomial #euler-maclaurin
54
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Find the development of a function $f(x)= x\cos^2(2x)$ in the power series in point $0$, and after that find derivative of $f^{(21)}(0)$

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#sequences-and-series #power-series #taylor-expansion #euler-maclaurin
56
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Find the Maclaurin Series for this particular function

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#calculus #taylor-expansion #euler-maclaurin
237
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Proving Euler-Maclaurin approximation for even functions using Poisson summation

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#fourier-transform #euler-maclaurin #poisson-summation-formula
148
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In what case(s) does the Euler-Maclaurin summation method yield the exact evaluation?

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#sequences-and-series #reference-request #euler-maclaurin
257
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Formula for $f(1) + f(2) + \cdots + f(n)$: Euler-Maclaurin summation formula

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#real-analysis #integration #summation #euler-maclaurin
420
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Euler Maclaurin Formula to prove $\zeta(0)=-\frac12$ and $\zeta(-1)=-\frac{1}{12}$

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#number-theory #analytic-number-theory #riemann-zeta #zeta-functions #euler-maclaurin
91
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Why do these two sums define functions that are asymptotically so close in value?

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#sequences-and-series #asymptotics #euler-maclaurin
32
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Integral of factional part

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#definite-integrals #fractional-part #euler-maclaurin
79
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Sum of Maclaurin series with centre 0

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#taylor-expansion #euler-maclaurin
52
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Can I use a 'known' Maclaurin series to find the sum of a given series if the series lower bound is not the same?

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#calculus #sequences-and-series #summation #taylor-expansion #euler-maclaurin
90
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Asymptotic series for $\ln\binom{x}{k}$ as $k\to\infty$

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#sequences-and-series #asymptotics #binomial-coefficients #gamma-function #euler-maclaurin

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