0
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0answers
30 views

Reference for power series

I would need some references for power series, Taylors series of elementary functions, derivation and integration of power series, convergence of sequences of functions and series of functions. The ...
1
vote
1answer
34 views

Not quite alternating series

Quite a lot of things are known about alternating power series $$ \sum_{n \geq 0} (-1)^n a_n x^n, \quad a_n > 0, $$ like closed-form expressions for well-chosen $a_n$ and so on. In a problem I'm ...
-1
votes
1answer
40 views

Can any one tell me the books for power series?

Can any one tell me the books for power series? I want to find the power series for sqrt(x). I surf on the internet but there is no success. So please tell me the name of the book where I can find ...
0
votes
1answer
63 views

Automata and power series

I am taking a class on Automata and Formal Languages and I need to solve an exercise, but I have no idea where to start from. It sounds like this: Decide the coefficients of the words in ...
1
vote
1answer
121 views

Applications of higher powers of trigonometric functions

I am after a reference (book, papers etc) about the practical applications of trigonometric functions raised to higher powers. An example is one that I have been using in my own studies: $\cos^4 ...
9
votes
1answer
164 views

Is this (classical?) exercice missing a hypothesis?

A friend just told me about an exercice he was given quite a few years ago, but he wasn't sure wether he remembered all the hypothesis correctly. Does anybody recognize this? Let $f$ be a smooth ...
1
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1answer
196 views

Exponential of formal power series and Bell polynomials

Wikipedia gives here the following formula for the exponential of a formal power series: $\exp \Big[\ \sum_{n=1}^\infty \frac{a_n}{n!} x^n\ \Big] = \sum_{n=0}^\infty \frac{B_n(a_1,\dots,a_n)}{n!} ...
1
vote
2answers
111 views

Problem regarding infinite sum of remainders.

Before here @math.SE there was a question regarding a problem on a maths magazine. I decided to look at the link provided, and one problem proposed was (if I'm not recalling this wrongly): Find ...
5
votes
2answers
248 views

Basic guidance to write a mathematical article.

I'm trying to put together a mathematical article on how to obtain certain infinite series for some well known functions by a method of integrals (I like to call it "The Integral Method" - thank you), ...
11
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1answer
458 views

Radius of convergence of power series

Given a meromorphic function on $\mathbb{C}$, is the radius of convergence in a regular point exactly the distance to the closest pole? As Robert Israel points out in his answer, that this is of ...