
ZOJ Problem Set  2628
Bessel function is one of the most important special functions in the field of physics. Many solutions of various physical phenomena have the form of this function. In mathematic notation, this function is deduced from the following differential equation:
There are two classes of solution of the above equation. One class of the solution (which is called the first kind of Bessel function) has the following image: Now you are asked to calculate Bessel function of the first kind using the above integral. Input: The input consists multiple test cases. In each test case, there are two numbers in one line, indicating the n and z in the above integral. (0<=n<=20, 0<=z<=20.0)Output: For each case, just output Jn(z). You must accurate the result up to 6 digits. Sample Input:0 0.00 10 11.11 20 19.99Sample Output: 1.000000 0.286025 0.164206 Author: FAN, Xiang Source: ZOJ Monthly, November 2005 