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How to find Taylor series for $\ln(1+2x)$ using power series of $\frac{1}{1-x}$

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#summation #power-series #taylor-expansion
37
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I want to know the interval of the convergence of the following power series.

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#convergence-divergence #power-series
54
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Tribonacci Numbers Satisfying Certain Conditions

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#sequences-and-series #power-series #fibonacci-numbers #square-numbers
64
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Another inequality with exponential sum and trigonometry

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#derivatives #trigonometry #inequality #power-series #exponentiation
50
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Which expression about power series is correct?

Published on
#power-series
52
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Find error for Taylor series

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#summation #power-series
281
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$f(z) = z + f(z^2)$ outside the unit disk?

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#complex-analysis #power-series #functional-equations #analytic-functions #analytic-continuation
98
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Prove that $\sum_{n=0}^{\infty}a_{n}b_{n}z^{n}=\frac{1}{2\pi i}\int_{\gamma_{r}}\frac{f(w)}{w}g(\frac{z}{w})dw$.

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#complex-analysis #power-series #complex-integration #cauchy-integral-formula
92
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Using power series prove that $\frac{d} {dx} e^{2x} = 2xe^{2x}$

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#calculus #sequences-and-series #derivatives #power-series
119
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How can one get an analytic continuation of a power series?

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#power-series #analytic-continuation
426
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Laplace Transform of $\cos \sqrt t$

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#trigonometry #power-series #laplace-transform
91
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Radius of convergence of power series where power increases by increments of 2

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#real-analysis #power-series
158
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Zeros of power series via Newton Polygons

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#power-series #p-adic-number-theory #newton-series
1.4k
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Solving $(4-x^2)y''+2y=0$ by series

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#sequences-and-series #ordinary-differential-equations #power-series
88
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Finding the area of convergence and sum function of complex series

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#sequences-and-series #complex-analysis #power-series

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