Bessel Definition and 249 Threads

Hi everybody ! Maybe this post should go under partial differential equations but I'm not sure... I have the following problem and I would like to know if someone could give me some hints or something to read related to this. I'm studying multiple reflections of acoustics waves in a...

I really have no idea. I started with the frobenius method. Until the recurrence formula. I got that already. But I just don't know where to plug in the 1/2 into the equation. Can anyone help? I just need to know where to put in the 1/2? Or can i use the normal bessel function which in...

Differntial equation involving bessel functions - pls help! 1. I am trying to simplify the expression in the attachment below to extract some data: https://www.physicsforums.com/attachment.php?attachmentid=18352&d=1239157280 2. the relevant equation for beta is given by...

Hi everyone, I need some help solving a bessel function of the 1st order. The equation is used to calculate the mutual inductance between two inductors. The equation is: M=(1.45*10^-8)*integral [J1(1.36x)J1(0.735x)exp(-13.6x)]dx the integral is from zero to infinity. Can someone help...

Hi, I am en electrical engineering grad student and I have to solve an equation to calculate the mutual inductance between an antenna and a micro-inductor. I think it is a Bessel equations but I don't know how to solve. M(a,b,d)=(1.45x10^-8)*integral(J1(1.36x)*J1(0.735x)*exp(-x-13.6))dx...

I am trying to solve int(int(exp(a*cos(theta)*sin(phi))*sin(phi), phi = 0 .. Pi), theta = 0 .. 2*Pi) (1) with a a constant. Using the second last definite integral on http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions the integral (1) reduces to...

Homework Statement By appropriate limiting procedures prove the following expansion \frac{1}{\left(\rho^2+z^2\right)^{1/2}}=\int^{\infty}_{0} e^{-k\left|z\right|}J_{0}(k\rho)dk Homework Equations The Attempt at a Solution I tried to implicate the fourier-bessel series but it...

Hi, I am working on the derivation of an equation on electrokinetic flow in microfluidic. I am stuck at a point that need me to do an integration in the form of r * cosh (Io(r)) where r = variable to be integrated I0 = zero order modified bessel function of the first kind Is there...

hallo, i now spent an hour looking for a formula connecting the modified bessel functions I_n and K_n to the hypergeometrical series F(a,b;c;z). has somedoby an idea? thank you

Homework Statement The Bessel function generating function is e^{\frac{t}{2}(z-\frac{1}{z})} = \sum_{n=-\infty}^\infty J_n(t)z^n Show J_n(t) = \frac{1}{\pi} \int_0^\pi cos(tsin(\vartheta)-n\vartheta)d\vartheta Homework Equations The Attempt at a Solution So far I...

Homework Statement Bessels equation of order n is given as the following: y'' + \frac{1}{x}y' + (1 - \frac{n^2}{x^2})y = 0 In a previous question I proved that Bessels equation of order n=0 has the following property: J_0'(x) = -J_1(x) Where J(x) are Bessel functions of...

Hello, I am in the process of showing that the modified Bessel function, I_v(x), is a solution to the modified Bessel equation, x^2*y''+x*y'-(x^2+v^2)*y=0 I have differentiated the MBF twice and plugged it into show that the left hand side is in fact 0. After a good amount of work...

I really need to prove eq. 10.1.45 and 10.1.46 of Abramowitz and Stegun Handbook on Mathematical functions. Is an expansion of e^(aR)/R in terms of Special Functions! Any help will be appreciated.

Hi everybody... i would like to seek help for the problem below. the assumptions I've considered is that transfer is radial only since it is a very long cylinder (infinitely long) that transfer in z direction is negligible, thermal radiation is zero, and wood properties are constant. Starting...

Hello, I am a researcher working on electromagnetic field. when solving the PDE equation, this integral about Bessel funtion arises: \int_{R1}^{R2} x J_1 (sx) dx where J_1 is the 1th order Bessel function of first kind, and s is a constant, R1 and R2 is integral interval. I have not...

Homework Statement I am attempting to solve the 2nd order ODE as follows using the generalized solution to the Bessel's equation Homework Equations original ODE: xd^{2}y/dx^{2}-3dy/dx+xy=0 The Attempt at a Solution My first thought is to bring out an x^-1 outside of the function so...

Hi, Do you have any idea to solve this integral? \int^{\phi_{1}}_{\phi_{2}} exp[j cos(x)] dx where \phi_{1} and \phi_{2} are an arbitrary angles. If \phi_{1}=\pi and \phi_{2}=0, the answer for this integral is a Bessel function. Thanks, Viet.

Homework Statement so, without typing the whole thing (because I do not know how to use any LaTeX or similar program) what is the domain for the Bessel function J(sub 1)(x) = ... Homework Equations I am to understand that taking the derivative of this monster will give me some kind...

Hi Guys, I'm an undergrad student...and i have a difficulty trying to solve 4xy" + 4y' + y = 0, and express the solution in term of Bessel function. I have tried Frobenius method...then...it didn't work..and I'm really confused Could anyone please help me with this?...i'd would really...

The following link: http://electron6.phys.utk.edu/QM1/modules/m1/free_particle.htm mentions something about the Bessel-Parseval relation... could someone explain what this is exactly and how it works?

hello every body ... I am a new member in this forums ..:smile: and i need ur help in telling me what's the perfect way to study legendre and bessel function for someone doesn't know anything about them and having a hard time in trying to understand ... i`ll be thankful if u...

I have a problem in electromagnetism giving a DE that looks something like a Lapacian or a Bessel function, I'm told. It derives from cylindrical coordinates. .\ \ \ \ \ \ \ \ \left( \partial_{r} ^2 + \frac{1}{r}\partial_{r} - \frac{1}{r^2}\right)E = \frac{1}{c^2}\partial_{t}^2 E\ \ \ \ \ \ \...

hello, while working on a problem i encountered the following integral :(limits are zero and infinity) Integral[J1(kR)dk] J1 is the first order bessel function..cudnt put 1 in subscripts.. Is there an analytical solution for this?? also is it possible to integrate it numerically...

To calculate a p.d.f. of a r.v., I need to integral a product of two bessel function as \mathcal{L}^{-1} \left( abs^2 K_n( \sqrt{as}) K_n( \sqrt{bs} ) \right) where \mathcal{L}^{-1} is the inverse Laplace transform. I think some properties about the bessel function can solve this...

Homework Statement I'm wondering if the bessel functions are pure real. What I really want to know is that if the bessel funtions are J and Y (i.e. first and second kinds), and the Hankel functions are H_1=J+iY and H_2=J-iY, then can we say that H_1=H_{2}^{*} where the * denotes complex...

Homework Statement Show that Jn(x+y) = ∑ Jr(x)Jn-r(y) ; where (Jn)= bessel function , ∑ varies from (-to+)infinity for r Jo(x+y) = Jo(x)Jo(y) +2 ∑ Jr(x)J-r(y) ∑ varies from (1 to infinity) for r Homework Equations The Attempt at a Solution I have solved the first...

Hi all, I am trying to find an expression for the values of the derivates of the Bessel-J_1 functions at two. The function is defined by J_1(x)=\sum_{k=0}^\infty{\frac{(-1)^k}{(k+1)!k!}\left(\frac{x}{2}\right)^{2k+1}} this I can differentiate term by term, finding for the n^th derivative at...

Hi This is one of the problems for my take home final exam on differential equations. I have been looking for a solution for this problem intensely for the last two days. This problem comes from Calculus vol 2 by Apostol section 6.24 ex 7. here it is Homework Statement Use the identities...

Hello Trying to calculate and simulate with Matlab the Steady State Temperature in the circular cylinder I came to the book of Dennis G. Zill Differential Equations with Boundary-Value Problems 4th edition pages 521 and 522 The temperature in the cylinder is given in cylindrical...

I have been working on this for some hours now. How can I prove Jsub2(x) = (2/x)*Jsub1(x) - Jsub0(x)??

If we want to find x giving J_m(x)=0 where m=any constants, how can we analytically get x? Thank you

bessel function please explain 1. Homework Statement summation limits (n=j to infinity) (-a/4)**n/n!(2n_ n+j) =(-1)**j e**(-a/2) I(a/2) where j>=1 the rest are constants and I is summation index i was just solving a SHM problem involving Fourier transform in which this happens to be one...

bessel function please explain this step Homework Statement summation limits (n=j to infinity) (-a/4)**n/n!(2n_ n+j) =(-1)**j e**(-a/2) I(a/2) where j>=1 the rest are constants and I is summation index i was just...

(Repost of thread, wrong forum). Hi all, I'm writing a simulation of Chladni plates in Max/MSP and hope to use it in granular synthesis. I have found two formulas on the web; square and circular plate. I understand the square but the circular is quite confusing as I'm not a mathematician...

What am I missing when I'm unsuccessful in showing by direct substitution into the spherical Bessel equation r^2 \frac{d^2R}{dr^2} + 2r \frac{dR}{dr} + [k^2 r^2 - n(n + 1)] R = 0 that n_0 (x) = - \frac{1}{x} \sum_{s \geq 0} \frac{(-1)^s}{(2s)!} x^{2s} is a solution? What's the catch??

Hi all, I was just wondering if anyone knew how to differentiate Bessel functions of the second kind? I've looked all over the net and in books and no literature seems to address this problem. I don't know if its just my poor search techniques but any assistance would be appreciated.

The Bessel function can be written as a generalised power series: J_m(x) = \sum_{n=0}^\infty \frac{(-1)^n}{ \Gamma(n+1) \Gamma(n+m+1)} ( \frac{x}{2})^{2n+m} Using this show that: \sqrt{\frac{ \pi x}{2}} J_{1/2}(x)=\sin{x} where...

I want to solve the partial differential equation \Delta f(r,z) = f(r,z) - e^{-(\alpha r^2 + \beta z^2)} where \Delta is the laplacian operator and \alpha, \beta > 0 In full cylindrical symmetry, this becomes \frac{\partial_r f}{r} + \partial^2_rf + \partial^2_z f = f - e^{-(\alpha r^2 +...

why for bessel equations, if n isn't an integer, you can have the solution y(x)=(c1)Jn(x) +(c2)J(-n)x but isn't true if n's an integer?

why does the v parameter in the bessel function x^2y``+xy`+(x^2-v^2)y=0 have to be real and nonegative?

Hello, I am a geologist working on a fluid mechanics problem. Solving the PDE for my problem, this Bessel integral arises: \int_{0}^{R} x^3 J_0 (ax) dx where J_0 is the Bessel function of first kind, and a is a constant. I haven't found the solution in any table or book, and due to...

I'm trying to show that the Bessel function of the first kind satisfies the Bessel differential equation for m greater of equal to 1. The Bessel function of the first kind of order m is defined by J_m(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{2^{m+2n}n!(n+m)!}x^{m+2n} = x^m...

Hello, I hope someone can show me where I got stuck/wrong. Verify that the Bessel function of index 0 is a solution to the differential equation xy" + y' + xy = 0. Note that my "<= 1" DOES NOT mean less than or equal to 1 but an arrow pointing to the left... it is said to be "equation 1"...

I'm supposed to show that J_0 (x) = \sum _{n=0} ^{\infty} \frac{\left( -1 \right)^{n} x^{2n}}{2^{2n} \left( n! \right) ^2 } satisfies the differential equation x^2 J_0 ^{\prime \prime} (x) + x J_0 ^{\prime} (x) + x^2 J_0 (x) = 0 Here's what I've got: x^2 J_0 ^{\prime...

Hello guys, i had a little chat with a teacher of mine and he asked me how can someone plot the zero order Bessel function. Here is what I've done.. using the integral expresion for J_{0}(r) J_{0}(r)=\frac {1}{\pi}\int_0^\pi \cos(r\cos\theta)d\theta i can calculate the first order...

Hi there ; I wanted you to help me with a problem. Well, I'm now studying griffiths' quantum book and now I'm trying the three dimensional schrodinger equation. I just wanted to know more about bessel functions. Can anyone give me a link for it? Some useful book will be good too. Thanks a...

I have the solution to a particular D.E. (Airy's D.E.) which is in terms of Airy functions, namely a linear combination of Ai(x) and Bi(x), to which I have to fit to the boundary conditions. Both Ai(x) and Bi(x) can be cast into a form which involves both modified Bessel functions of the first...

Hey guys I was wondering if you could help me out with a proof of the recursion relations of Bessel functions on my homework: Show by direct differentiation that J_{\nu}(x)=\sum_{s=0}^{\infty} \frac{(-1)^{s}}{s!(s + \nu)!} \left (\frac{x}{2}\right)^{\nu+2s} obeys the...

What role do Bessel functions play in frequency modulation theory?