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Results tagged with ca.classical-analysis-and-odes
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user 1162
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
votes
Is the following function decreasing on $(0,1)$?
This is more of a long comment to the remark in GH's answer. I did some calculations regarding the expression
$$-\frac{q}{1-q} - \sum_{n=1}^{\infty} \frac{8nq^{4n}}{1-q^{4n}} + \sum_{n=1}^{\infty}\fra …
- 2,154
18
votes
4
answers
3k
views
Is the following function decreasing on $(0,1)$?
Hi,
I asked some time ago the following question on math.stackexchange, but I ask it here too since it remains unanswered.
The question concerns a function I encountered during research :
$$f(k):= …
- 2,154
1
vote
1
answer
142
views
On the geometry of roots of a sum of complex linear fractions
I was wondering if there is anything known about the geometry (position) of the roots of a rational map of the form
$$R(z):= \sum_{j=1}^{n} \frac{a_j}{z-p_j},$$
where the $a_j$'s are nonzero complex n …
- 2,154
3
votes
2
answers
391
views
Is this infinite series related to some well-known special functions?
Please allow me to resort once again to the expertise of the MathOverflow community :
During research I encoutered the following infinite series :
$$\sum_{n=-\infty}^{+\infty} \frac{u^{2n}}{1+\rho^{ …
- 2,154
8
votes
Which sequences can be extended to analytic functions? (e. g., Ackermann's function)
Actually, there is an even stronger result, often called the interpolation
theorem, which follows from a well-known theorem of Mittag-Leffler:
Let $(z_n)$ be a sequence of complex numbers with no lim …
- 2,154
7
votes
Reference for complex analysis jargon
I really recommend the book Potential Theory in the complex plane"
by Thomas Ransford.
It's a very nice book with exercises and it covers each of the 5 points you mentioned.
- 2,154