1
vote
4answers
72 views

closed-form term for this sum:

related to this question: Is there an easy closed-form term for $$\sum_{j=k}^{\infty} \frac{x^j}{j!}e^{-x},$$ thus when the sum starts at a constant $k$ instead of $1$? EDIT: Thanks for your help. ...
0
votes
0answers
43 views

can´t solve this kind of exponential equations

I have no clue how can i solve this kind of exponential equation in closed form: $a^n - b^n \le c$ where $a > 1$ and $-1 < b < 0$ thank you very much for your help
1
vote
0answers
97 views

How to solve these exponential equations for D?

I'm curious if this is even possible to solve for D. D is the only variable, x, y, z, and w are all constants, and e is the mathematical constant e. $$ (\frac{x+yD^{2}}{zD})^{\sqrt{2D}} = ...
4
votes
3answers
356 views

How do I find if $\frac{e^x}{x^3} = 2x + 1$ has an algebraic solution?

Is there some way of solving $$\frac{e^x}{x^3} = 2x + 1 $$ non-numerically? How would I go about proving if there exists a closed form solution? Similarly how would I go about proving if there exists ...