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Taylor series representation of Planck's law

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#calculus #taylor-expansion
155
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A Question concerning the definition of Analytic functions

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#analysis #power-series #taylor-expansion #definition #analyticity
141
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Solve the limit of the sucession $ \left(1+\frac{1}{2}\right) \left(1+\frac{1}{4}\right) \times \dots \times \left(1+\frac{1}{2^n}\right) $

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#taylor-expansion
354
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Why are all analytic functions equivalent to their Taylor series?

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#real-analysis #analysis #power-series #taylor-expansion #analyticity
2.1k
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Proving $\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{2n-1}x^{2n-1}$ is differentiable

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#calculus #real-analysis #derivatives #power-series #taylor-expansion
1.7k
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Using a Taylor polynomial to calculate the error in using $x$ as an approximation for $\sin{x}$

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#calculus #power-series #taylor-expansion
67
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How to obtain the taylor series of $\frac{1}{\cos x}$ up to the 6th order term?

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#taylor-expansion
2.7k
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Lagrange Inversion Theorem Proof

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#taylor-expansion #residue-calculus #hypergeometric-function #polylogarithm #lagrange-inversion
181
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Exponential convergence of Taylor series.

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#real-analysis #sequences-and-series #convergence-divergence #power-series #taylor-expansion
34
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Taylor polynomial and formula for remainder

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#real-analysis #taylor-expansion
42
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A question about nonparametric (kernel function) estimation

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#probability #probability-theory #taylor-expansion #statistical-inference #infinitesimals
49
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$e^{-\frac{1}{x^2+y^2}}$ is $C^\infty$ and Taylor polynomial.

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#real-analysis #multivariable-calculus #derivatives #taylor-expansion
59
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Let $f(x)=(2+x+ax^2)\ln (1+x)-2x$ with $f(x)$ achieving its maximum value at $x=0$. Find $a$.

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#calculus #optimization #taylor-expansion
32
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Changing indexing of an infinte series

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#sequences-and-series #complex-analysis #taylor-expansion #infinite-product
602
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Taylor remainder in integral form

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#calculus #real-analysis #integration #power-series #taylor-expansion

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