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Find radius of convergence for a complicated series for $f'(f(x)) = f(f'(x))$

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#sequences-and-series #complex-analysis #power-series #taylor-expansion #functional-equations
45
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Determining sum of series

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#power-series #taylor-expansion
48
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Taylor series of $e^x$

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#taylor-expansion
1.2k
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How to find the 5th degree Taylor polynomial about x = 0

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#calculus #sequences-and-series #taylor-expansion
54
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When does the convergence of Taylor coefficients imply pointwise convergence?

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#complex-analysis #taylor-expansion #uniform-convergence #pointwise-convergence
109
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Expanding a function undefined at zero.

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#calculus #power-series #taylor-expansion #laurent-series
95
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Prove inequality $0< \frac{1}{n} \ -\ln\left( 1+\frac{1}{n} \right) < \frac{1}{2n^{2}}$ using Taylor polynomial

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#calculus #inequality #logarithms #taylor-expansion
32
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Role of $f(\mathbf{x}_0)$ and $\nabla f(\mathbf{x}_0)^T (\mathbf{x} - \mathbf{x}_0)$ in quadratic approximation

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#multivariable-calculus #optimization #taylor-expansion #positive-definite #positive-semidefinite
53
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Series with Taylor

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#calculus #sequences-and-series #taylor-expansion
276
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$O(h^3)$ in the second-order approximation for $f(\mathbf{x}^*)$

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#multivariable-calculus #optimization #asymptotics #taylor-expansion #approximation
2.3k
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Taylor series of $e^{-z^2}$ around $z_0=0$

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#complex-analysis #taylor-expansion
31
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Solution verification: $f(x)=\frac{x^2}{(x^3-4)^{\frac13}}$ series expansion at positive and negative $\infty$

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#real-analysis #asymptotics #taylor-expansion #solution-verification #binomial-theorem
105
Views

Why is $x(\log(x)-1)+1\geq \frac{1}{4}(x-1)^2$ in a neighborhood of $x=1$?

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#calculus #taylor-expansion
493
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Taylor Polynomial with E

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#calculus #taylor-expansion
73
Views

Taylor Series inverse function

Published on
#calculus #functions #summation #taylor-expansion

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