SoS problem in legendre and bessel functions

[thebigstar25]

hello every body ... I am a new member in this forums ..




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 show me what to do or giving me tips make me understand how to deal
with problems containg difficult integrals involving these two functions ...

 

[AstroRoyale]

Have a look at Arfken and Weber, "Mathematical Methods for Physicists", there are lots of sections on special functions in there.

 

[thebigstar25]

thanks alooooooooot ... but i have one more request ..

if there is anyone knows a website that shows examples for the legendre and bessel functions please let me know ...


and thanks in advance ...

 

[Dick]

wikipedia and mathworld are always reasonable first references. Just google either. But I don't think from an applied point of view either of these subjects are particularly worthy of special study. They are just 'special functions' that come out of differential equations. Put your time into studying differential equations in general.

 

[thebigstar25]

thanks Dick ... i think u r right i should begin with the differential equations ...

the problem with me is my major is physics and there is subject ^mathematical methods in physics^


and i didnt take before anything related to this subject that's why i don't know what to do
and how to study ...

 

[Dick]

Don't worry. You'll learn. There are whole courses devoted to trig functions. There's a gazillion other families of similar functions. But you don't have to know so much about them. Find a reference you like and keep it handy to look things up. If you ask me on the street what I know about In(x) and Yn(x), it's not much. But I know where to look them up. That's what counts. I used a big blue Dover book by Abramovitz and Stegen.

 

[thebigstar25]

thanks again Dick ... I am so nervous because its the first time i feel lost in a subject ..

i like when i study something to understand where it came from not just applying a theorem
and having no idea from where it came ...

i guess for now i`ll do what u had told me .. and after i finish the course i`ll look for more
details related to what i had in this subject and try to understand it ..

 

[Dick]

When you finish the course you'll know what's important to remember and what's not. The second category is a lot bigger than the first.

 

[thebigstar25]

ok Dick one last question ... when i try to solve problems involving these functions and include integrals how can i start the answer ?

 

[Dick]

Post an example.

 

[thebigstar25]

for example :-


show that :-


Jn(x) = 1/pi integral from zero to infinity ( cos(n theta - x sintheta ) ) d theta

 

[Dick]

You only want the integral from 0 to pi. I would try substituting the integrand into the bessel equation and try to integrate the result from 0 to pi. If you get zero then it solves the bessel equation. Now check boundary conditions.

 

[thebigstar25]

ammmm i tried it but it gets even harder than the one that is solved ... they start solving it by using the summation of both the sine and cosine then substitute it in the integral ..

for me i don't know it doest make sense .. why they specially used this method instead of another methods .. how its going to come to my mind starting the solution like this ..

 

[Dick]

You have to be creative. That's all I can say. There aren't many areas of math that include a rule book that solves all problems. You learn through experience.

 

[thebigstar25]

thanks Dick for the tips ... I am going to try harder this time and be creative and i hope it will work with me :) ...