 Site Statistics  |   Contact  |   About Us       Tuesday, September 21, 2021  ~ Laguerre Method ~ Hermite Method ~ Chebyshev Method ~ Bessel Method

 "Special Functions" Hermite Polynomial Method
 Results = x = -1.00, H20(x) = 1107214478336 x = 0.00, H20(x) = 670442572800 x = 1.00, H20(x) = 1107214478336 x = 2.00, H20(x) = 5080118660096 x = 3.00, H20(x) = 59990281399296 x = 4.00, H20(x) = 619678016654336 x = 5.00, H20(x) = -2.25717767163827E+17

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

IMPLEMENTATION
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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