Question

2. Legrendre polynomials are sometimes used in applied mathematics. The first 3 Legrendre polynomials are: , Pi(x)-x, P2(x) = 2 For i> 2 subsequent Legrendre polynomials may be generated by the following formula: Pi = (2 * i-1) * x *P1-(i-1)*P-2 Let x = 0.66. Using VBA, calculate P2 through P10 using a For loop. Begin with and turn in a owchart with your solution.

Answer 1

VBA Code:

Public Function Legendre(n As Integer, x As Double) As Double
'Computes the nth Legendre polynomial given x

Dim Pn As Double, Pn_1 As Double, Pn_2 As Double
Dim j As Integer
If n < 0 Then
MsgBox "n must be >= 0. Error"
Legendre = 0
Exit Function
End If
'P0 is 1 and P1 is x.
If n = 0 Then
Pn = 1
ElseIf n = 1 Then
Pn = x
Else 'n >= 2
Pn_1 = 1
Pn = x
For j = 2 To n
Pn_2 = Pn_1
Pn_1 = Pn
Pn = (((2 * j - 1) * x * Pn_1) - ((j - 1) * Pn_2)) / j
Next j
End If
Legendre = Pn
End Function

Flowchart:

Function execution results:

Description:

As stated in the problem using values from P0(X), P1(X) and formula for  Legendre equation used a for loop to implement the value assignment for Pn(X) and displayed the results.