
100  Let's Celebrate the 100th Contest on ZOJ!  100G
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 second kind of Bessel function) has the following image: Now you are asked to calculate Bessel function of the second kind using the above integral. InputThe input consists multiple test cases. In each test case, there are two numbers in one line, indicating the v and z in the above integral. (0≤v≤20, 1≤z≤20.0) OutputFor each case, just format and print Y_{v}(z) in "%.6le". See sample for more details. Sample Input0 1.00 1 4.00 10 11.11 20 20.00 Sample Output8.825696e02 3.979257e01 1.797017e01 2.854895e01 HintYou may want to solve to the problem Bessel Function first. Author: WU, Zejun Source: Let's Celebrate the 100th Contest on ZOJ! 