16
votes
1answer
219 views

Approximate value of a slowly-converging sum of $\sum|\sin n|^n/n$

In this question on Math.SE there appears this sum: $$ S = \sum_{n\geq1}s_n, \qquad s_n = \frac{|\sin n|^n}{n}, $$ which converges very slowly. What methods would you suggest for evaluating it ...
0
votes
2answers
150 views

Solutions of $ \frac{1- x^{\alpha}}{1- x^{\beta}} = \gamma$

Would it be possible to give pieces of information about $x \in \left]0,1\right[$ such that: $$ \frac{1- x^{\alpha}}{1- x^{\beta}} = \gamma$$ where $\alpha > 0$, $\beta > 0$ and $\gamma > ...
-2
votes
1answer
124 views

Integral question: zeroes of the primitive.

Let $z$ be a complex number. Let $f(z)$ be an elementary function but not a polynomial. Let its integral $F(z)$ be impossible to express in elementary functions. If we define $F(z)$ as $\int$ from $A$ ...
1
vote
1answer
105 views

Algorithms for finding closed form approximations for integrals (with no closed form solutions)

It is well known that many integrals have no closed form solutions, normally what you would do is solve them numerically. My question is if there are algorithms that give you good closed form ...
3
votes
2answers
101 views

Is there an algebraic solution to $e^{-x/a}+e^{-x/b}=1$ ($a\neq b$, $a,b$ constants)?

Is there an algebraic solution for the to find the intersection of the following two functions for values of $x\geq 0$: $$f_1(x)=1-2e^{-x/a}=f_2(x)=-1+2e^{-x/b}$$ $a$ and $b$ are positive constants. ...