0
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1answer
14 views

Some questions about series and generalized integrals

Do someone of you know any good site about generalized integrals and series (convergence and divergence) with example exercises with detailed solutions ? I would be happy if you did know any. My ...
0
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2answers
34 views

Power Series - Reference Request (?)

I'm not sure if I've tagged that correctly as a reference request or not, but I'm nearly done with Kenneth Ross's book Elementary Analysis, and one of the topic's that's caught my interest to learn ...
0
votes
1answer
28 views

Zeros of polynomials and power series

Consider $k_i \in \{-1,1\}$ for every $i \in \mathbb{N}$ and consider the family of polynomials $P$ of the form $$\mathop{\sum}\limits_{i=0}^n k_it^i;$$ and the family of power series $S$ of the form ...
0
votes
0answers
33 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
35 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
41 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
128 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
166 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
vote
1answer
229 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
113 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
253 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
votes
1answer
489 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 ...