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Sum identity using Stirling numbers of the second kind

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#combinatorics #summation #power-series #stirling-numbers
116
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Definite integral and remainder using three terms of a power series

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#calculus #power-series
81
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Series - Product of Exponential Function with Confluent Hypergeomtric Function

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#sequences-and-series #power-series #hypergeometric-function #cauchy-product
24
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When is Ration of Power not continous

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#real-analysis #continuity #power-series
6.3k
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Uniform Convergence of Power Series

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#power-series #uniform-convergence
1.1k
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Power series to evaluate a definite integral of $f(x)=\frac1{1+x^7}$

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#sequences-and-series #definite-integrals #power-series
208
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Functional equation: $f(x)=x+\dfrac{f(2x)}{f(3x)}$

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#functions #power-series #functional-equations #continued-fractions
143
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Is the function $P_m(x) = 2^mx + 3^mx^2 + ... +p_n^mx^n +...$ mathematically useful? Does it converge to known constants for rational m and x?

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#calculus #real-analysis #sequences-and-series #prime-numbers #power-series
38
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Puzzling Trinomials and validity

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#sequences-and-series #power-series #binomial-theorem
339
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Continuity of $\limsup$ related to Cauchy-Hadamard formula

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#continuity #power-series #limsup-and-liminf #banach-algebras
490
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Analytic continuation of $\sum z^{2n}$

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#complex-analysis #power-series #analytic-continuation
184
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Closed form for probabilities from generating function of queue length in M/D/1 queue.

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#probability-theory #stochastic-processes #power-series #generating-functions #queueing-theory
99
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Finding the coefficient of $x^r$ in exponential series: $\frac{e^{nx}-1}{1-e^{-x}}$

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#algebra-precalculus #power-series #exponentiation #closed-form
78
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Is there a simple series representation for following sequence?

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#sequences-and-series #numerical-methods #power-series #taylor-expansion
86
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What is the resulting big oh for this expression?

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#real-analysis #sequences-and-series #asymptotics #power-series

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