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Write $\int\frac{1-\cos x}{x}dx$ as power series

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#real-analysis #power-series #indefinite-integrals
109
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Find $\int_{0}^{1} \cos x^{2} \operatorname dx$ as power series and compute with $10^{-4}$ accuracy

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#real-analysis #power-series
71
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Refinement inequality of : $\sqrt{x}+x^{\frac{x}{x+1}}\geq x+1$

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#limits #inequality #power-series #exponentiation #a.m.-g.m.-inequality
37
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What is the power series of $1/(D-h(x))$ if $h(x)\ll D$?

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#sequences-and-series #power-series #taylor-expansion #approximation #linear-approximation
73
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Taylor Series of $f(x) =\frac{1}{x^2}$

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#calculus #power-series #taylor-expansion
71
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Knowing the expansion of a function, how can we find its expansion using the inverse of x?

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#sequences-and-series #power-series #taylor-expansion
68
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Prove that an inequality holds for $\alpha \ge 2$

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#limits #inequality #power-series #exponentiation
54
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convergence radius of $\displaystyle{\sum_{n=0}^{\infty}}(\sqrt{ 4^n +3^n}＋ (-1)^n\sqrt{ 4^n-3^n})x^n$

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#real-analysis #analysis #power-series
41
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How do we prove that $\int_0^1 (x\ln x)^{-1+n}\,dx = -\left( -\frac{1}{n} \right)^n \Gamma(n)$

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#calculus #sequences-and-series #power-series #taylor-expansion #gamma-function
125
Views

Sum with reciprocal general term.

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#power-series #formal-power-series
28
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$\frac{w_k}{x-x_k}$ expansion into decreasing powers of $x$

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#calculus #power-series
550
Views

Sums of reciprocals of powers of the imaginary part of the nontrivial zeros of the Riemann zeta function

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#sequences-and-series #number-theory #polynomials #power-series #riemann-zeta
66
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Convergent power series and Euclidean domain, or field.

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#abstract-algebra #ring-theory #field-theory #power-series
47
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On the convergence of particular power series

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#real-analysis #sequences-and-series #power-series
178
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Cauchy product of two formal power series

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#power-series #analytic-functions

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