Welcome to ZOJ
100 - Let's Celebrate the 100th Contest on ZOJ! - 100G
Bessel Function II

Time Limit: 5 Seconds      Memory Limit: 65536 KB

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:

Because of its importance in the physics and it cannot be expressed by elementary functions, many formulas are deduced to numerically calculate it. The following integral is one of them.

Now you are asked to calculate Bessel function of the second kind using the above integral.


The 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)


For each case, just format and print Yv(z) in "%.6le". See sample for more details.

Sample Input

0 1.00
1 4.00
10 11.11
20 20.00

Sample Output



You may want to solve to the problem Bessel Function first.

Author: WU, Zejun
Source: Let's Celebrate the 100th Contest on ZOJ!
Submit    Status