User Claude Leibovici

10 votes

Is anything known about the series $\sum_{n=0}^{\infty} x^{\sqrt{n}} $?

answered Aug 5, 2022 at 4:58

9 votes

Roots of this sextic

answered May 25, 2023 at 6:02

8 votes

Roots of polynomials of particular type

answered Aug 10, 2020 at 8:05

7 votes

Accepted

Generalized harmonic numbers and Riemann zeta function

answered Jan 10 at 14:58

6 votes

Locating the maximum point $x_n$ of $f_n(x):=e^{-1/x}\Bigl(1+\frac{1}{n^2 x^n} \Bigr)$ in $(0,1)$

answered Jan 25, 2023 at 15:34

6 votes

Identity involving Pochhammer symbol

answered Jan 29 at 10:52

5 votes

Accepted

What are the local maxima and minima of $\frac{\sin(nx)}{\sin(x)}$

answered Jan 17 at 6:44

4 votes

Surprisingly long closed form for simple series

answered May 15, 2022 at 9:13

4 votes

For a manual evaluation of a definite integral

answered Jan 20 at 7:27

4 votes

Accepted

How to prove approximation for fresnel integral converges

answered Apr 8, 2023 at 7:50

4 votes

Evaluating the series $\sum_{n=0}^{\infty} n! x^n$ and inverse variable-fractional-derivatives

answered Aug 16, 2022 at 9:17

3 votes

Accepted

Expression of the inverse function of $f(x)=e^{-\varepsilon x}\sinh(x)$

answered Oct 6, 2022 at 12:14

3 votes

Rigorous estimates on roots of function

answered Dec 13, 2022 at 11:55

3 votes

Approximation of pseudogeometric progression

answered Apr 13, 2023 at 2:40

3 votes

How fast does this summation grow?

answered May 29, 2023 at 7:33

3 votes

What's the summation of formal series $\sum_{n\geq0}\binom{n\delta}{n}x^n$？

answered Jan 25 at 2:50

2 votes

limit of definite integral as $N \to \infty$

answered Feb 5 at 11:39

2 votes

Solving an equation involving $x$ both squared and inside a logarithm

answered Jan 18 at 10:02

2 votes

Asymptotics of error function integral with square root

answered Jan 19 at 14:19

2 votes

Does the integral $\int_0^{\infty}e^{cx^2+dx}dx/(a+bx)$ have a closed form?

answered Jan 21 at 8:23

2 votes

Definite integral of Bessel function of the first kind times $x^{3/2}$

answered Jan 22 at 12:33

2 votes

Asymptotics of an integral requested

answered Apr 20, 2023 at 11:53

2 votes

Is it possible to solve this integral?

answered Feb 5, 2023 at 8:56

1 vote

Asymptotics of the unique root of a polynomial equation defined as a sum of rational expressions

answered Feb 16, 2023 at 12:51

1 vote

Accepted

What's this infinite sum?

answered Mar 22, 2023 at 15:21

1 vote

Limiting values of particular functions

answered Feb 3, 2023 at 11:28

1 vote

attempt improve rational approximation against Pade aproximation

answered May 25, 2023 at 5:35

1 vote

Some Log integrals related to Gamma value

answered Jan 7, 2023 at 10:14

1 vote

Approximation of the sum involving binary entropy function

answered Dec 19, 2021 at 5:04

1 vote

Approximating exp(x) with a piecewise-linear function accurately

answered Feb 20, 2022 at 8:13

Stack Exchange Network

42 Answers

Is anything known about the series $\sum_{n=0}^{\infty} x^{\sqrt{n}} $?

Roots of this sextic

Roots of polynomials of particular type

Generalized harmonic numbers and Riemann zeta function

Locating the maximum point $x_n$ of $f_n(x):=e^{-1/x}\Bigl(1+\frac{1}{n^2 x^n} \Bigr)$ in $(0,1)$

Identity involving Pochhammer symbol

What are the local maxima and minima of $\frac{\sin(nx)}{\sin(x)}$

Surprisingly long closed form for simple series

For a manual evaluation of a definite integral

How to prove approximation for fresnel integral converges

Evaluating the series $\sum_{n=0}^{\infty} n! x^n$ and inverse variable-fractional-derivatives

Expression of the inverse function of $f(x)=e^{-\varepsilon x}\sinh(x)$

Rigorous estimates on roots of function

Approximation of pseudogeometric progression

How fast does this summation grow?

What's the summation of formal series $\sum_{n\geq0}\binom{n\delta}{n}x^n$？

limit of definite integral as $N \to \infty$

Solving an equation involving $x$ both squared and inside a logarithm

Asymptotics of error function integral with square root

Does the integral $\int_0^{\infty}e^{cx^2+dx}dx/(a+bx)$ have a closed form?

Definite integral of Bessel function of the first kind times $x^{3/2}$

Asymptotics of an integral requested

Is it possible to solve this integral?

Asymptotics of the unique root of a polynomial equation defined as a sum of rational expressions

What's this infinite sum?

Limiting values of particular functions

attempt improve rational approximation against Pade aproximation

Some Log integrals related to Gamma value

Approximation of the sum involving binary entropy function

Approximating exp(x) with a piecewise-linear function accurately