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Show that $r^l, r^{-l-1}$ are solutions to $\frac{1}{R}\frac{d}{dr}\left(r^2\frac{dR}{dr}\right)=l(l+1)$

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#ordinary-differential-equations #proof-verification #power-series
1.2k
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Important identities that can be obtained by manipulating the function $\frac{x}{e^x-1} = \frac{B_0}{0!} + \frac{B_1}{1!}x + \frac{B_2}{2!}x^2 + ...$?

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#calculus #complex-numbers #power-series #intuition #generating-functions
3.8k
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Radius of convergence $\cos^{2}x$

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#power-series #taylor-expansion
78
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If $g(x)=\sum_{n} f_n x^n=\frac{2x^2+x^3}{1-x-x^2}$,then find the general expression for the coefficients,$f_n$.

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#complex-analysis #power-series #analyticity #holomorphic-functions #analytic-functions
80
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Radius of convergence

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#convergence-divergence #power-series
34
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How to express the function $a(t)$ knowing a parametrization $a(\eta)$ and $t(\eta)$?

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#functions #differential-geometry #power-series #taylor-expansion #parametric
27.9k
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infinite summation of exponential functions

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#sequences-and-series #limits #power-series #exponential-function
43
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Legal operation in limit summation?

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#sequences-and-series #limits #power-series #exponential-function
1k
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Find the values of $x$ for which the series converges

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#calculus #power-series
92
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How to compute exponent series

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#sequences-and-series #power-series
761
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$.99999...=1$: What is the proof that we can multiply an infinite series by something to shift it?

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#sequences-and-series #power-series #infinity #proof-explanation
690
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Product between an infinite and a finite power series

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#linear-algebra #power-series #products
769
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How can we know the answer to 1-1+1-1+1...?

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#power-series
527
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How to prove a power series can be analytically continued?

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#complex-analysis #power-series
1.3k
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Generalizing Variant Proof of Basel Problem

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#sequences-and-series #polynomials #power-series

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