q1 ask and ancer
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material propertiesTRANSCRIPT
Q1:
given that and , and determine ,,and .Solution:-
Q2 : Derive Rodrigues formula By Legendre polynomials are given by
Now integrating this n times from 0 to x, we obtain
Which can be written
or
Which proves that.
Q3: prove that
Using the binomial theorem
We have
And the coefficient of in this expansion is
Which can be written as
i.e the required result thsult thus follows
Q4: Using the Rodrigues formula to determine and .Solution:-
Q5: determine Legendre polynomials
Solution:-
,,
(a)
+
From (a):-
Let m=m-2
m=n
m=n-2
Polynomial c0,c1x,c0(1-3x2),c1(x- x3)P0(x)=1c0=1P1(x)=xc1=1P2(x)=1-x2=1-3x2c0=-1/2
P3(x)=x- =x- x3c1=-3/2
P4(x)=1- +=1-10 x2+ x4c0=3/8
P5(x)= x- x3+ x5=x- x3+ x5c1=15/8
P6(x)=1-x2+ x4-
Q6: Find
Q7: Using Power series to solve Legendre's Equation :-
Whit n=3 & n=5, Find Legendre Polynomials
K=0,1,2,3,
n=2,4,6
n=5
Q8 : find a solution In the interval -0.5