Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with hypergeometric-functions
Search options answers only
not deleted
user 82588
Hypergeometric functions are the analytic functions defined by Taylor expansions of the shape $\sum_{n \geq 0} a_n x^n$, where $a_{n+1}/a_n$ is a rational function of $n$. This general family of functions encompasses many classical functions. The hypergeometric functions play an important role in many parts of mathematics.
6
votes
Hypergeometric function evaluation 4F3
From https://dlmf.nist.gov/15.4 one has
$$
\sum_{k=0}^n\frac{(1/3)_k(-1/3)_k}{k!(1/2)_k}(-z^2)^k=\frac{1}{2}\left(\left(\sqrt{1+z^{2}}+%
z\right)^{2/3}+\left(\sqrt{1+z^{2}}-z\right)^{2/3}\right)
$$
an …
- 5,624
13
votes
Accepted
Yet another real-rooted polynomial
First, we write the polynomial in hypergeometric form
$$
Q_{m,n}(t)=\frac{(-1)^{m+n+1} \Gamma (m+n-t+1) }{\Gamma (-t) \Gamma (m+n+2)}\, _3F_2\left({-m,-n,m+n-t+1\atop 1,-t};1\right).
$$
Applying Thoma …
- 5,624
4
votes
Accepted
Double Series involving Gamma function
This problem can be reduced at least formally to a compact double integral, which might be easier to solve.
Starting with the integral representation for the Gamma function, we write the double sum a …
- 5,624
3
votes
Accepted
On $x^k+y^k=1$ and the Dixonian elliptic functions
Define the generalized trigonometic functions (discussion of these functions is given in this answer)
$$
z=\int_0^{\sin_{pr}z}\frac{dt}{\sqrt[p]{1-t^r}},\qquad \cos_{pr}z=\sqrt[r]{1-(\sin_{pr}z)^r},\q …
- 5,624