The Rodrigues formula for generating the Legendre polynomial is given by Pn (T) = = 1 dn Generate the first ten Legengre polynomials to find the orthogonal set [1 2n! dan [(x²-1)].

Q: Construct a divided-difference table for f(x) = cos(x) based on the five points (k; cos(k)), for k =…

A: To form the divided difference table, use the following formulae.…

Q: A monic cubic polynomial has zeros 2 and (-1)/2±√11/2 i. Find the polynomial.

A: Given zeros are 2, -12±112i let a=-2, b=-12+112i, c=-12-112i let x be the variable of the…

Q: Show that the Chebyshev polynomials have thefollowing properties: Tm(Tn(x)) = Tmn(x)

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Q: The first three Legendre polynomials are 1, x, and x2 - ½. Choose c so that the fourth polynomial x3…

A: The first three Legendre polynomials are 1,x,x2-12. The fourth polynomial is x3-cx which is…

Q: 2. Find all of the prime quadratic polynomials in F4[x], where F4 {0,1, a, b} be the field of four…

A: Given: F4={0,1,a,b}

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Write down monic polynomials in R[X] of least possible degree which have the following complex…

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Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

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Q: List all the polynomials of degree 2 in Z2[x]. Which of these areequal as functions from Z2 to Z2?

A: We know that a polynomial of degree 2 has the representation fx=ax2+bx+c, where a, b and c are…

Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

A: We have to interpolate f(1) using Newton's Divided Difference Formula.

Q: for which value of L are the legendre polynomial orthogonal on [ -L, L ]  interval? also find || P2…

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Q: The fourth degree Taylor polynomial for f(z) = 1 centered at a = -3 is T(z) = co +q(x+3) + c(r + 3)2…

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Q: Show that every polynomial of degree at least 1 takes every complex value a E C.

A: We have to prove that every polynomial of degree atleast 1 takes every complex value a in C .

Q: Calculate the first three Legendre coefficients for f (x) = x2 - 1 and then express the f(x) in…

A: Recall the definition of Legendre polynomials.

Q: Compute the first 5 Legendre Polynomials, Po(x), P₁(x), -P₁(x). (These These are > Solutions, P,…

A: What is Legendre Polynomial: Legendre polynomial is a collection of orthogonal polynomials of degree…

Q: A 6th degree polynomial with roots at: x=1, x+1= 2  Square root 3, X=3+i

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Q: Find the integration distance (f, 9) = | f(x)g(x) dæ between the given polynomials. f(x) = 11æ – 3,…

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Q: Consider the homogenous polynomial ai + 10r1r2 + x². Find a suitable substitution s = Question 3 azi…

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Q: a) Show that x = 1+2i is a root of p(x) where i = surds(-1). b) By using the fact that p(x) is a…

A: We have to solve given problem:

Q: factor x as a product of three linear polynomials in Z/30Z[x] by using Chinese remainder theorem

A: Ans- To factor x as a product of three linear polynomials in Z/30Z[x], we first need to factor 30…