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How does doing a Fourier Transform affect a functions' power series representation?

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#analysis #soft-question #fourier-analysis #power-series
77
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Prove that a power series satifies that $x^2y''-4xy'+(x^2+6)y=0$

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#ordinary-differential-equations #power-series
75
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I need toSolve this proof for complex numbers

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#calculus #sequences-and-series #complex-analysis #complex-numbers #power-series
1.3k
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Laurent series of $f(z)=\frac{1}{z^{2}\sinh(z)}$

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#sequences-and-series #complex-analysis #analysis #power-series #laurent-series
104
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Solve $\lim_{x \to 1} x^{\frac{1}{1-x}}$ using Taylor's expansion

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#limits #power-series #taylor-expansion
71
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Infinite sum power series

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#sequences-and-series #summation #power-series #binomial-coefficients #infinity
366
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Radius of convergence for binomial series

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#sequences-and-series #convergence-divergence #power-series #binomial-theorem
59
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Radius of convergence of $\sum_{n = 0}^\infty a_nx^n $ when $a_n = 1$ if n is a perfect square and $a_n = 0$ otherwise

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#real-analysis #sequences-and-series #analysis #convergence-divergence #power-series
25
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Stepping through a power series, I would like to keep the sum of terms the same with different step sizes

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#power-series
58
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Maclaurin series for $f(x) = \frac{x-cosa}{1 - 2xcosa + x^{2}}$

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#calculus #sequences-and-series #power-series #taylor-expansion
463
Views

If a series converges to zero, does this imply that the leading terms are zero? Or under what conditions would this be necessary?

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#real-analysis #sequences-and-series #convergence-divergence #power-series #taylor-expansion
142
Views

Convergence of power series cannot contain pole

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#complex-analysis #power-series
55
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A closed form for these non-elementary, generalized relatives of the geometric series

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#sequences-and-series #analysis #power-series #closed-form #theta-functions
85
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Series Expansion and Big-Oh Notation: Expanding $\sqrt{x^2+\mathcal{O}(x^3)}$ to get $x+\mathcal{O}(x^{3/2})$

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#asymptotics #power-series #taylor-expansion #binomial-theorem
87
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Is there a way to represent functions using circles, similar to how Taylor series work?

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#power-series #taylor-expansion #circles #approximation

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