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How to find value of arctan using Maclaurin

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#euler-maclaurin
186
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6th Degree Polynomial and Chebyshev minmax

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#polynomials #taylor-expansion #chebyshev-polynomials #euler-maclaurin
423
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How to integrate the "fractional part"/sawtooth function?

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#integration #riemann-zeta #ceiling-and-floor-functions #fractional-part #euler-maclaurin
81
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Maclaurin polynomial error bounds

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#polynomials #taylor-expansion #rounding-error #euler-maclaurin
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the remainder of Maclaurin Series

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#power-series #euler-maclaurin
454
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Bounds for Periodic Bernoulli Polynomials via Fourier Series

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#fourier-series #bernoulli-numbers #euler-maclaurin #bernoulli-polynomials
352
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Numerical integration of sharply peaking function: $\int_0^{1000} \exp(1000\sin(x)/x)\,{\rm d}x $

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#calculus #integration #taylor-expansion #statistical-mechanics #euler-maclaurin
950
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Using the Euler-Maclaurin formula to approximate Euler's constant, $\gamma := \lim_{n\to\infty}\left(-\ln n+\sum_{k=0}^n\frac1n\right)$

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#numerical-methods #harmonic-numbers #euler-mascheroni-constant #euler-maclaurin
595
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Are the partial sums for $\sum_{n=1}^{\infty}\sin(n^a)$ bounded for $a\geq1$ and unbounded for $0<a<1$?

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#calculus #sequences-and-series #trigonometric-series #euler-maclaurin
181
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Integral involving the fractional part function

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#integration #fractional-part #euler-maclaurin
155
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Taylor series of functions

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#power-series #taylor-expansion #hyperbolic-functions #euler-maclaurin
72
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Convergence of sum to integral

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#sequences-and-series #riemann-sum #euler-maclaurin
167
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Anyone knows how to calculate the sum of this series?

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#sequences-and-series #summation #logarithms #taylor-expansion #euler-maclaurin
269
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Proof That $\sum_{k=1}^{n-1}\int_{k}^{k+1}\left\{x\right\}f´(x)dx=\int_{1}^{n}\left\{x\right\}f´(x)dx$

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#integration #summation #euler-maclaurin #ramanujan-summation
77
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The nth term of the maclaurin sequence of $\frac 1{1+x+x^2}$

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#sequences-and-series #combinatorics #binomial-coefficients #euler-maclaurin

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