User kevinkayaks

5 votes

1 answer

177 views

Turning sum into integral when the widths of the intervals are not uniform

asked Aug 22, 2021 at 17:12

4 votes

1 answer

241 views

Compound Binomial-Exponential: Closed form for the PDF?

asked Dec 14, 2018 at 22:18

4 votes

1 answer

198 views

nonlinear ODE's involving heaviside step functions: The bouncy ball as an example

asked Aug 8, 2021 at 1:21

3 votes

2 answers

168 views

Roll a sphere over two other spheres which it contacts

asked May 27, 2017 at 14:14

3 votes

2 answers

352 views

Closed form for an infinite series involving lower incomplete gamma functions

asked Jul 25, 2019 at 18:35

2 votes

0 answers

40 views

How to solve for the operator such that $\hat{O} e^{-a x} = a^{-1/2} e^{-a x} $?

asked May 30, 2021 at 20:51

2 votes

1 answer

190 views

Inverse Fourier transform of $\exp(A \operatorname{sinc} (B t) )$

asked Feb 17, 2021 at 19:18

2 votes

0 answers

149 views

Fokker-Planck approximation of birth-death process -- solution of non-linear ODE

asked Dec 23, 2019 at 17:55

2 votes

0 answers

31 views

Solution of a vector PDE $\partial_t W = A(x) W(x,t) + B(x) \partial_x W$

asked Nov 3, 2021 at 20:24

2 votes

0 answers

59 views

Why does a matrix PDE $ \hat{M}_{ij}(t) v_j(t) = 0$ imply $| \hat{M}_{ij}(t) | (v_1(t)+v_2(t)+\dots) = 0$?

asked Feb 25, 2022 at 22:32

2 votes

0 answers

78 views

Can I solve a diffusion equation in a bounded geometry by the Laplace transform method?

asked Jan 19, 2022 at 20:31

2 votes

0 answers

27 views

Asymptotic behavior of telegrapher's equation by neglecting various terms

asked Jan 23, 2022 at 23:38

1 vote

0 answers

42 views

First order non-linear inhomogeneous ODE: $\dot{x}(t) = a(x) + b(t)$

asked Feb 20, 2022 at 1:12

1 vote

0 answers

35 views

Inverse Laplace transform of $ \frac{1}{s}\frac{1}{1 + (k/s)^a + (l/s)^b}$

asked Apr 4, 2022 at 23:11

1 vote

1 answer

31 views

Gaussian white noise evaluated at a function: $\xi(f[t])$

asked Oct 26, 2022 at 19:47

1 vote

0 answers

70 views

Approximate solution to $\epsilon y'' + x^2 y' - \lambda y = 0$ near $x=0$

asked Feb 21 at 1:15

1 vote

0 answers

39 views

The functional ODE $(x \partial_x + a x^2 - b x + 1) f(x) = f(q x)$

asked Mar 8, 2022 at 19:45

1 vote

1 answer

96 views

The limit as $\epsilon \rightarrow 0+$ of $\frac{1}{\epsilon}P\big(\frac{u}{\epsilon}\big)$

asked Mar 11, 2022 at 0:31

1 vote

0 answers

26 views

An integral approximation for $Q = \sum_x f(x) $ when $\tan(C x) = x$

asked Dec 25, 2021 at 22:39

1 vote

0 answers

141 views

Divergence when calculating moments with a space-time Gaussian white noise

asked Feb 16, 2021 at 3:41

1 vote

0 answers

21 views

Large $t$ solution to $\partial_t S(x,v,t) = v \partial_x S + (a+v) \partial_v S + \partial_v^2 S$

asked Jan 12, 2022 at 5:06

1 vote

2 answers

78 views

fIs it possible to solve the D.E. $f''(x) + a(x) f'(x) + bf(x) = 0 $ for arbitrary $a(x)$?

asked Sep 23, 2021 at 21:37

1 vote

0 answers

30 views

Why can we split product averages of stochastic processes? $\langle x(t_1)x(t_2)\dots x(t_N) \rangle = \langle x(t_1)x(t_2)\rangle \dots$

asked Oct 20, 2021 at 19:37

1 vote

0 answers

26 views

Strange splitting issue with finite difference simulation of telegraph-type equation: $W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0$

asked Oct 23, 2021 at 23:21

1 vote

1 answer

45 views

$k$ derivatives of $f(x)^p$

asked Oct 2, 2019 at 4:25

1 vote

0 answers

12 views

Transforming $0 = D u P''(u) - (D+G u)P'(u) + (G-Vu)P(u)$ to a standard form? [duplicate]

asked Nov 8, 2020 at 22:31

1 vote

1 answer

62 views

Laplace method for $\int_0^1 dx x^\gamma \frac{\partial}{\partial x} P\big(\frac{u}{x}\big) $ where $\gamma \gg 1$ and $P(\infty)\rightarrow 0$

asked Nov 15, 2020 at 22:04

1 vote

0 answers

49 views

Functional Differential Eq. $ y''(x) - A y'(x) - B y(x) + \alpha B y(\alpha x)= 0$

asked Nov 18, 2020 at 2:56

1 vote

1 answer

85 views

The integrals $\frac{1}{2\pi} \int_{-\infty}^\infty\frac{ e^{-i z u}}{z \pm i c }dz $

asked Nov 22, 2020 at 22:37

1 vote

1 answer

198 views

Expanding convolution integrals for sharply-peaked functions.

asked Dec 13, 2020 at 4:44

Stack Exchange Network

61 Questions

Turning sum into integral when the widths of the intervals are not uniform

Compound Binomial-Exponential: Closed form for the PDF?

nonlinear ODE's involving heaviside step functions: The bouncy ball as an example

Roll a sphere over two other spheres which it contacts

Closed form for an infinite series involving lower incomplete gamma functions

How to solve for the operator such that $\hat{O} e^{-a x} = a^{-1/2} e^{-a x} $?

Inverse Fourier transform of $\exp(A \operatorname{sinc} (B t) )$

Fokker-Planck approximation of birth-death process -- solution of non-linear ODE

Solution of a vector PDE $\partial_t W = A(x) W(x,t) + B(x) \partial_x W$

Why does a matrix PDE $ \hat{M}_{ij}(t) v_j(t) = 0$ imply $| \hat{M}_{ij}(t) | (v_1(t)+v_2(t)+\dots) = 0$?

Can I solve a diffusion equation in a bounded geometry by the Laplace transform method?

Asymptotic behavior of telegrapher's equation by neglecting various terms

First order non-linear inhomogeneous ODE: $\dot{x}(t) = a(x) + b(t)$

Inverse Laplace transform of $ \frac{1}{s}\frac{1}{1 + (k/s)^a + (l/s)^b}$

Gaussian white noise evaluated at a function: $\xi(f[t])$

Approximate solution to $\epsilon y'' + x^2 y' - \lambda y = 0$ near $x=0$

The functional ODE $(x \partial_x + a x^2 - b x + 1) f(x) = f(q x)$

The limit as $\epsilon \rightarrow 0+$ of $\frac{1}{\epsilon}P\big(\frac{u}{\epsilon}\big)$

An integral approximation for $Q = \sum_x f(x) $ when $\tan(C x) = x$

Divergence when calculating moments with a space-time Gaussian white noise

Large $t$ solution to $\partial_t S(x,v,t) = v \partial_x S + (a+v) \partial_v S + \partial_v^2 S$

fIs it possible to solve the D.E. $f''(x) + a(x) f'(x) + bf(x) = 0 $ for arbitrary $a(x)$?

Why can we split product averages of stochastic processes? $\langle x(t_1)x(t_2)\dots x(t_N) \rangle = \langle x(t_1)x(t_2)\rangle \dots$

Strange splitting issue with finite difference simulation of telegraph-type equation: $W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0$

$k$ derivatives of $f(x)^p$

Transforming $0 = D u P''(u) - (D+G u)P'(u) + (G-Vu)P(u)$ to a standard form? [duplicate]

Laplace method for $\int_0^1 dx x^\gamma \frac{\partial}{\partial x} P\big(\frac{u}{x}\big) $ where $\gamma \gg 1$ and $P(\infty)\rightarrow 0$

Functional Differential Eq. $ y''(x) - A y'(x) - B y(x) + \alpha B y(\alpha x)= 0$

The integrals $\frac{1}{2\pi} \int_{-\infty}^\infty\frac{ e^{-i z u}}{z \pm i c }dz $

Expanding convolution integrals for sharply-peaked functions.