(1- 2xt + t?) = (x-t)(x,t) (1) at ag (1- 2xt + t) t g(x,t) (2) ax ag t= (x - t) ag at (3) ere g(x,t) is the generating function of Legendre's polynomials Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) P-n Pn-1

Q: The recurrence relation for the differential equation xy + 2y -xy=0 is Oack(k+r)(k+r-1)-Ck-2=0…

A: Let y= ∑k=0∞akxk+r be the solution of the given differential equation.Here y1= ∑k=0∞ak(k+r)xk+r-1…

Q: 1- Prove the following relations: ag (1 – 2xt + t?)= (x - t) g(x, t) (1) at ag (1- 2xt + t2)= t g(x,…

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Q: Consider the Legendre polynomials of degree n Ph(x) = Σ (-1)m 0<m< where n is a nonnegative integer…

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Q: If the Legendre polynomials P5 63 x5-70 x3 +15 x then: %3D Find 1) , x* Ps(x) dx 2) P',(-1) A) L*…

A: Given: To explain the correct option of the given statement as follows,

Q: 2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁).…

A: Given that   that interpolate then we have Now  ,       putting

Q: his is some (a) Use this

A: Given  (a) y" + 3y' + 2y = f(t), y(0)=y'(O)=0. (b)f(t) = e3t and f(t) = t.

Q: Suppose P(z) is a polynomial satisfying • P( – 4) = - 32 • P'( – 4) = 44 • P''( – 4) = – 90 • P(3) (…

A: The polynomial function P(x) where polynomial is a function of x , input any value of x the value of…

Q: (5) Compute -2 67 using Euler's criterion.

A: Objective: To compute -267. Concept used: Euler's criterion, is a result from number theory that…

Q: x² Vx² + 1 .2 Expand In in terms of In x, In(x² + 1) and In(x+ 1). (x+ 1)7

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Q: 2 0] Find the characteristic polynomial of A =-1 0 1 0 1 1 2

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Q: The first three Hermite polynomials are Ho(x) = 1, H₁(x) polynomials are defined using the inner…

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