Hilbert’s Tenth Problem (HTP) is the question raised by David Hilbert at his famous 1900 Paris lecture on whether or not there is an algorithm to decide whether a Diophantine equation has a solution over the integers:

## 22.7.11

## 19.7.11

### Java Code examples - Bernoulli polynomial function

/**

* return nth Bernoulli polynomial of x using Fourier expansion

* ref: Abramowitz & Stegun 23.1.16 pp 805

* @param n

* @param x

* @return

*/

**public static ****double **BernoulliP (**int **n, **double **x)

{

// for n>1, 1>=x>=0

// for n=1, 1>x>0

// for x=0 return the nth Bernoulli number

**if **(x==0.0) {

**return **BernoulliB(n);

}

**double **K = -2*(factorial(n))/StrictMath.pow((2*StrictMath.PI), n);

**double **S = 0.0;

**for **(**int **k=1; k<100001; k++)

{

S +=

StrictMath.cos((2*StrictMath.PI*k*x)-(.5*StrictMath.PI*n))/

StrictMath.pow(k, n);

}

**return **K*S;

}