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 |
33
votes
Accepted
What is the indefinite sum of tan(x)?
I add more details for the solution in the distinguished answer due to Anixx. First, we need the digamma function
http://en.wikipedia.org/wiki/Digamma_function
which we will call $\Psi(x)$. Importan …
7
votes
Accepted
Convergence of Newton series for sin ax
half-discrete analytic
First do the formal calculation, then discuss its validity.
$$\begin{align}
&\sum_{m = 0}^{\infty} \binom{x}{m} \sum_{k = 0}^{m} \binom{m}{k} (-1)^{(m - k)} \operatorname{sin} …
6
votes
What is the indefinite sum of tan(x)?
There is no reason to think there is any simple expression for solution $T$ of
$$T(x + 1) - T(x) = \tan(x)$$
What we CAN find a simple solution to is this:
$$T(x + \pi) - T(x) = \tan(x)$$
3
votes
Convergence of Newton series for sin ax
weak discrete-analytic
Closed form here involves some ${}_2F_1$ functions, so I cannot provide proofs. Numerically, though, it seems that $\sin(ax)$ is weak discrete-analytic for $a$ up to some valu …