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Closed form of the power series of $\sum_{n=0}^{\infty} \sin(n)\,x^n$ (Mathematica)

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#sequences-and-series #complex-analysis #power-series #taylor-expansion
575
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Show that if $X$ is a bounded random variable, then its characteristic function is a power series with an infinite radius of convergence.

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#probability #probability-theory #measure-theory #power-series #characteristic-functions
704
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Power series and intervals of convergence

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#calculus #convergence-divergence #power-series
131
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Why doesn't the $x^k$ function series converge in -1?

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#convergence-divergence #power-series
116
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Sum of a geometric series over natural density zero indices

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#number-theory #prime-numbers #power-series #summability-theory
31
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Comparing remainder(residual) Rn(x)

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#power-series #taylor-expansion
74
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Maclaurin series of $\exp(-ab^2 x^2+2abc x)$

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#power-series #taylor-expansion #normal-distribution
1.5k
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Power series and partial fractions

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#calculus #power-series #formal-power-series
59
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Complex numbers series

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#sequences-and-series #complex-analysis #complex-numbers #power-series #divergent-series
90
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Convergence radius with series

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#sequences-and-series #complex-analysis #convergence-divergence #power-series #divergent-series
1.2k
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Can the quantum harmonic oscillator be solved by power series methods without going for asymptotic analysis?

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#calculus #ordinary-differential-equations #asymptotics #power-series #quantum-mechanics
56
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Explaining why there is no power series $f(z)=\sum^{\infty}_{n=0}C_{n}z^{n}$

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#complex-analysis #power-series
21
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Coefficient of degree $-1$ in $df/f$

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#derivatives #power-series
697
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Taylor series for $\ln(x+4)$ about $x=-1$

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#calculus #sequences-and-series #power-series #taylor-expansion
83
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What does it mean for a power series to be 'defined' in this context?

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#real-analysis #functional-analysis #convergence-divergence #power-series

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