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Mean-value theorem for function of matrices

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#matrices #taylor-expansion #matrix-calculus #scalar-fields #mean-value-theorem
154
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Taylor Series - approximation of $\sin(x)$

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#calculus #sequences-and-series #taylor-expansion
125
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Approximation by Taylor expansion

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#real-analysis #taylor-expansion #power-series #approximation
144
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A Taylor expansion at $x_n$

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#derivatives #taylor-expansion #numerical-calculus
88
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maximizing Lagrange error on given interval by common sense?

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#taylor-expansion
63
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How to determine the precision of intermediate results in a calculation process?

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#sequences-and-series #taylor-expansion #numerical-calculus #rounding-error #significant-figures
68
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Kummer's Fourier expansion for $\ln\Gamma(x)$ derivation: cosine integral series expansion

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#taylor-expansion #fourier-series #special-functions
131
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How do I calculate this limit using power series?

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#calculus #limits #taylor-expansion #power-series
146
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Binomial Expansion error approximation

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#calculus #sequences-and-series #taylor-expansion
177
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Polynomial solution to differential functional equation of roots

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#calculus #polynomials #complex-numbers #taylor-expansion #functional-equations
73
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Absorbing integral boundaries

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#real-analysis #calculus #integration #taylor-expansion
94
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Newton Method Error Bound

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#taylor-expansion #upper-lower-bounds #newton-raphson
144
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What is the best bound for $f'$ knowing bounds on $f$ and $f'''$?

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#analysis #derivatives #taylor-expansion #interpolation-theory
56
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Linear term for a self consistent integral equation

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#integration #taylor-expansion #approximation
43
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Suppose that $|f(x)|\le1$ and $|f'''(x)|\le3$ for any $x\in \mathbb{R}$. Prove that $|f'(x)|\le 3/2$ for any $x\in \mathbb{R}$.

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#real-analysis #inequality #taylor-expansion

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