New posts in exponential-function

Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$

sequences-and-series exponential-function

Solving $x^{x^x}=c$ with Lambert's W function

exponential-function special-functions lambert-w

How would you explain why "e" is important? (And when it applies?) [duplicate]

exponential-function

Prove $\exp(x+y) = \exp(x) \exp(y)$ for $\exp(x) = \sum_{n=0}^\infty \frac {x^n}{n!}$

real-analysis sequences-and-series exponential-function

Approximate $\sqrt{e}$ by hand

calculus sequences-and-series algebra-precalculus exponential-function recreational-mathematics

$\int_{- \infty}^{\infty} \frac{f(x)}{1+\exp{g(x)}}dx=\int_{0}^{\infty} f(x) dx$ for $f(x)=f(-x),~g(x)=-g(-x)$ - are there other formulas like that?

integration definite-integrals exponential-function

Formula for compounding interest with yearly increasing additional payments

exponential-function finance

How to prove $ \lim_{n \to \infty} e^n \cdot \left( \sum_{k=0}^{n-1} ({k-n \over e})^k/k! \right)- 2 \cdot n = \frac 23$?

calculus sequences-and-series exponential-function

Prime consequences [closed]

sequences-and-series prime-numbers power-series exponential-function

Calculate the integral $\int e^{\sin x}\,dx$

calculus integration exponential-function indefinite-integrals substitution

Comparing Factorials vs 2^n

exponential-function factorial

Which of the following powers is bigger: $2^{41}$ or $3^{24}$?

arithmetic exponential-function

Find the number of real roots of $1+x/1!+x^2/2!+x^3/3! + \ldots + x^6/6! =0$.

polynomials taylor-expansion exponential-function roots

Solving $x^k+(x+1)^k+(x+2)^k+\cdots+(x+k-1)^k=(x+k)^k$ for $k\in\mathbb N$

number-theory summation exponential-function

On the pseudo-Fibonacci and pseudo-Tribonacci sequences $A_n = \lceil e^{(n-1)/2}\rceil $ and $B_n = \lceil e^{\pi(n-1)/5}\rceil $

sequences-and-series exponential-function fibonacci-numbers ceiling-and-floor-functions

Are exponential functions fractals?

exponential-function fractals

Invert the softmax function

probability exponential-function machine-learning logistic-regression

Exponential of powers of the derivative operator

analysis taylor-expansion exponential-function lie-algebras partial-derivative

Is there a simple proof that $e^2$ is irrational using a positional numeral system?

exponential-function irrational-numbers number-systems

Exponential Function as an Infinite Product

calculus real-analysis limits functions exponential-function