All Questions
3 questions
4
votes
1
answer
387
views
$\sum_{k=1}^n\frac{\sin kx}{k^\alpha} >0\quad\text{for all}\ n=1,2,3,\ldots\ \text{and}\ 0<x<\pi, \text{and}\ \alpha \ge 1$
The Fejer-Jackson inequality as follows:
$$\sum_{k=1}^n\frac{\sin kx}k>0\quad\text{for all}\ n=1,2,3,\ldots\ \text{and}\ 0<x<\pi.$$
I conjecture that the inequality as follows holds:
$$\sum_{...
- 1,776
2
votes
1
answer
662
views
Clausen’s identity for associated Legendre polynomials
Clausen’s identity for Legendre polynomials has the form (see, for example,
A generating function of the squares of Legendre polynomials, by Wadim Zudilin: https://arxiv.org/abs/1210.2493)
$$P_n(\cos{\...
- 16.5k
0
votes
1
answer
125
views
A slight generalization of triconfluent Heun equation: what is known?
I have recently come across an ODE of the form
$$y''+(a+b x^2)y'+(c+dx+h/x^2)y=0 \hspace{30mm} (*)$$
where $y=y(x)$ and $a,b,c,d,h$ are arbitrary constants.
As far as I understand (please correct ...
- 312