Ron Zamir

13 Questions 5 Answers 0 Followers

Questions related from Ron Zamir

Is there an exact solution to this integral?

I am trying to exactly solve the following integral: Integral from 0 to infinity of dw[e^(-Tw^2)(wcos(aw)+Hsin(aw))(wcos(bw)+Hsin(bw))/(w^2+H^2)], where T, a, b, and H are real numbers that are...

14 February 2024 5,818 3 View

Can you suggest references for solving integrals in the complex plane that involve Bessel functions?

I am looking for references that discuss how to solve integrals in the complex plane that involve Bessel functions. Any suggestions would be very much appreciated.

14 February 2024 3,721 1 View

When do BesselJ[nu, ax] and BesselY[nu, ax] cross over from their small-argument approximation to their large-argument approximation?

BesselJ[nu, ax] has as its small-argument approximation ([(ax)/2]^(nu))/Gamma[nu + 1], and has as its large-argument approximation (2/((pi)(ax)))^0.5*Cos[ax - (pi)/4 - nu(pi)/2]. BesselY[nu, ax]...

01 January 2022 6,901 1 View

How does the Diffusion Coefficient D depend on the dimension of the space in which the diffusion is occurring?

The Diffusion Coefficient D, for the regular diffusion of a particle in 1 dimension, is defined as D=sigma2/(2(delta t)), where sigma2 is the standard deviation squared of the particle's position,...

02 August 2021 2,578 4 View

Does there exist a closed form expression for a sum involving Sin and odd integers?

Does there exist a closed form expression for the following sum: Sum over n from 0 to infinity of: Sin((2n+1)(pi)(a))/((pi)(2n+1))^(2k+3), where a is a real number from 0 to 1, and k is an...

09 June 2021 4,837 3 View

Can a function be expanded using a basis of exponential functions e^(nx), where n is an integer?

Functions can be expanded in powers of x (Taylor series), or in Fourier series using cos(nx) or sin(nx) as a basis (where n is an integer). Can functions also be expanded using a basis of...

13 February 2021 1,972 3 View

Does there exist a polynomial approximation for e^(-x) when x>2 that is accurate and doesn't involve many Taylor terms?

Usually, when trying to evaluate e^(-x), its Taylor series is used. This is e^(-x) = Sum over n from 0 to infinity of (-x)^n/n! . However, when x>2, many Taylor series terms are needed to...

31 December 2020 8,723 3 View

Does there exist an asymptotic expansion for a cross product of Bessel Functions when k does not equal 1?

A Cross Product of Bessel Functions that I am interested in is of the form Jnu(z)Ynu(kz)-Jnu(kz)Ynu(z), where Jnu(z) and Ynu(z) are Bessel functions of the first and second kinds of order nu, and...

23 May 2020 257 3 View

What is the Fundamental Solution to the Diffusion Equation in 2d polar coordinates?

The Diffusion Equation in 2d rectangular coordinates is: dc/dt = D(d^2c/dx^2 + d^2c/dy^2), where c is the concentration, and D is the Diffusion Constant. A fundamental solution of this 2d...

19 July 2019 3,650 8 View

What is the method of proving that two different solutions of the same diffusion equation problem should be identical?

When solving problems involving the diffusion equation, (which in one dimension is dc/dt = D(d^2c/dx^2), where c is the particle concentration, D is the diffusion constant, and x and t are space...

11 June 2019 1,460 5 View

How do you express e^(-x) in terms of an ordinary MeijerG function?

I am interested in expressing e^(-x) in terms of an ordinary MeijerG function. I used the MeijerGReduce command in Mathematica 11.3 and found that e^(-x) can be expressed in terms of a...

01 October 2018 8,580 0 View

Why should two-particle coalescence and many particle coalescence have the same kinetics in 1d?

When two identical diffusing and absorbing particles are placed in 1d space, their survival probability S(T) is a well known function of the dimensionless time T=(Dt)/(xo)^2, (where D is the sum...

27 September 2018 213 1 View

Does a Green's Function exist for the heat equation for a certain geometry?

I am interested to know if there exists a Green's Function for the Heat Equation which depends on the cylindrical coordinates r and theta, and which satisfies Dirichlet Boundary Conditions (at...

05 July 2017 6,769 1 View