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Hermite Polynomial Method
Results =

Order of Hermite Polynomial:

[ Initial Order of Hermite Polynomial: {20) ]
[ Initial entries number: {7} ]

Hermite Polynomial Method

The Hermit polynomials are defined by:

Hn(x) = (-1)n ex 2 dn / dxne-x2

The first three Hermite polynomials are:

H0(x) = 1
H1(x) = 2x
H3(x) = 4x2 - 2

The Hermite polynomial satisfy the following recurrence relation:

Hn + 1(x) = 2xHn(x) - 2nHn - 1(x)

Testing the Hermite Polynomial Method

To test the Hermite Polynomial method, a new static method has been added. The implementation of these type of polynomials are based on their recurrence relation. The TestHermitePolynomial() method has been written, added and executed:

           static void TestHermitePolynomial();
                 for (int i = 0; i < t2; i++)
                     double x = 1.0 * i - 1.0;
                     ListBox1.Items.Add(" x = " + x + ".00, " + "H" + t1 + "(x) = " + SpecialFunctions.Hermite(x, t1).ToString());

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