EDIT: tHE QUESTION CAN BE SEEN HERE:
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Hey guys, im having a problem with using taylor's theorem. Well actually i dont know where to start. I need to use taylors theorem to find the value of the BESSEL FUNCTION OF ORDER 1 of J(1->5)(0) where J(x) Σ k=0-->∞
(-1)^k x^2k+1/ k!(k+1)! 2^2k+1
(scroll down for real translation)
So i guess i need to find the 1st 5 terms of this. But the only kind of taylors we have been taught is starting with a function and deriving. This starts with an infinite series so i dont know how to approach this. Sorry its a little bad looking so let me know if you need any clarification. Thanks!
Chris
A Bessel function of the first kind is a solution to the differential equation:
which are nonsingular at the origin. Bessel functions are commonly seen when solving electrostatic (or magnetostatic) equations in cylindrical coordinates. (Though they are seen in many other places as well.)
There is a recurrence relation for these Bessel functions:
That will allow you to compute the derivatives for your Taylor series.
I would look up Bessel functions on the web or in a book (I'm using Mathematical Methods for Physicists by Arfken) as it appears your instructor is expecting you to look up this information. (Note: I have not given you everything you need to find your Taylor series.)
-Dan
Topsquark, thanks and yea i did see that info online which ive been searching. But i still dont know how to relate any of the info to what i know of taylors theorem. Ive been taught to start with a normal function and find the derivatives and 4-5 terms or so. So i really have no clue