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Taylor polynomial of $\frac{1}{2-x}$

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#calculus #taylor-expansion
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Is there an expression for $\exp\left(t z^{i}\partial_{z}^{j} \right) f(z) = $?

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#operator-theory #taylor-expansion
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What is the rate of convergence of $\lim\limits_{h\rightarrow 0}\frac{\sin(h)}{h}=1$?

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#convergence-divergence #taylor-expansion
216
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Evaluating $\lim_{x \to 0}\frac{(1+x)^{1/x} - e}{x}$

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#calculus #limits #taylor-expansion #closed-form
643
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Infinite series expansion of $\arcsin (x)$ and $\arccos (x)$

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#calculus #taylor-expansion
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Sum of Taylor Series

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#sequences-and-series #summation #taylor-expansion
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Use of taylor series in convergence

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#convergence-divergence #numerical-methods #taylor-expansion
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Convergence of Taylor series about centre of open disc for analytic function.

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#complex-analysis #taylor-expansion #analyticity
6.1k
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Does the Taylor series of an infinitely differentiable function converge; and if yes, does it converge to the function?

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#real-analysis #taylor-expansion #analyticity
216
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Taylor expansion of $x^{1/x}$

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#taylor-expansion
465
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How to derive Maclaurin series for ln(1+x) without calculus?

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#taylor-expansion
939
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Quantum translation operator

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#operator-theory #physics #taylor-expansion #quantum-mechanics
104
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Find the Taylor expansion of $\frac{1}{x^2+2x-3}$ around $x=-1$.

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#calculus #sequences-and-series #taylor-expansion
188
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(Taylor's theorem) Proving that $\sin(x) = \sum\limits_{n=0}^{\infty}\dfrac{(-1)^{n}x^{2n+1}}{(2n+1)!}$

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#summation #taylor-expansion
1.5k
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approximation of x=sin(x) error

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#taylor-expansion #approximation #error-function

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