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Bessel is a very simple program which calculates the Bessel function of the first kind of real argument x and integer order n. ie. Jn(x)
To use it, all you do is start the program, and at the prompt enter the integer ORDER and the real ARGUMENT.
Values of Order and Argument up to 50 are acceptable.
All digits displayed are significant.
For the record, Bessel functions are solutions of Bessel's differential equation. They are useful in FM radio work, and when working with circular waveguide.
In FM radio, when the argument X is equal to the FM modulation index the n'th sideband corresponds to the n'th order bessel function of X. The carrier amplitude is proportional to the zero'th order bessel function of X {J0(x)}
The program computes the J bessel function for real argument, and integral order, using the recurrence relation : Jn-1(x)=(2*n/x)Jn(x)-Jn+1(x), and the normalization factor from: J0(x)+2*J2(x)... = 1.0 Refer to the NBS HANDBOOK OF MATHEMATICAL FUNCTIONS, PAGE 385. Domain: The program is good for arguments up to 50, and order (n) up to 50. All figures printed are significant.