from arfken Rework Example 10.3.1 by replacing фп(x) by the conventional Legendre polynomial. Pn (x): [Pn...
From Arfken, demostrate equation 12.85. Step by step solution please. Associated Legendre Polynomials The regular solutions, relabeled pn (x), are (12.73c) These are the associated Legendre functions.16 Since the highest power of x in Pn (x) is xn, we must have m n (or the m-fold differentiation will drive our function to zero) In quantum mechanics the requirement that m n has the physical interpretation that the expectation value of the square of the z component of the angular momentum...
2. Show that the following is true of the Legendre polynomial : Pn(1) = 1 V n=1,2,3,... Hint: Use Rodrigues' Formula and recall that (x² - 1) = (x + 1) (x - 1) so that you can employ the Product Rule from calculus.
Legendre polynomial 7. Using the Legendre polynomials given by Px(x) = 2mm. An (x2 - 1)" evaluate (a) [ P3(x)dt (b) | 1-1 P2(2) In(1 - 0)dc Hint: Use integration by parts after computing P2() and P3().
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of degree 0 and 1, 3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of...
Answer True or False and explain 1 The infinite family {Pn(x)}^=o of Legendre polynomials Pn(x) forms a complete orthogonal family on the interval [-1, 1]. If we delete the first element Po(x) = 1 from the set, the remaining family {Pn(x)}=1 also forms a complete orthogonal set. 2 Let {Xn}n=1 be a complete orthogonal family of functions for the vector space L[0, 1]. Then enlarging the set by adding to this set the vector 2X5 + 3X18, we end up...
A polynomial p(x) is an expression in variable x which is in the form axn + bxn-1 + …. + jx + k, where a, b, …, j, k are real numbers, and n is a non-negative integer. n is called the degree of polynomial. Every term in a polynomial consists of a coefficient and an exponent. For example, for the first term axn, a is the coefficient and n is the exponent. This assignment is about representing and computing...
Example 6.3 from Textbook. ONLY CALCULATE THE ENTROPY As discussed in the class, derive the best fit polynomial (preferably quadratic) equation to perform the integration. Don't use the area under the curve rule as used in the textbook to find the integral value. Compare your results with textbook answers. Example 6.3: Calculate the enthalpy of saturated isobutane vapor at 360 K from the following information: (1) compressibility-factor for isobutane vapor; (2) the vapor preschire of isobutane at 360 K is...
Question 4 [12 marks] Some applications of mathematics require the use of very large matrices (several thousand rows for example) and this in turn directs attention to efficient ways to manipulate them. This question focuses on the efficiency of matrix multiplication, counting the number of numerical arithmetic operations (addition, subtraction and multiplication) involved. We start with very simplest case of 2x2 matrices. (a) The standard way of multiplying 2x2 matrices uses 8 multiplications and 4 additions. List the 8 products...
The first two parts should be solved by Matlab. This is from an intro to Numerical Analysis Class and I have provided the Alog 3.2 in below. Please write the whole codes for me. Alog3.2 % NEWTONS INTERPOLATORY DIVIDED-DIFFERENCE FORMULA ALGORITHM 3.2 % To obtain the divided-difference coefficients of the % interpolatory polynomial P on the (n+1) distinct numbers x(0), % x(1), ..., x(n) for the function f: % INPUT: numbers x(0), x(1), ..., x(n); values f(x(0)), f(x(1)), % ...,...
Suppose X1, .., Xn is a random sample from a N(0, a2) population, where variance o are known. Consider testing Ho : 0 = O0 vs. Hi 0 700 Q1(4pt): Using Likelihood Ratio Test (LRT) to obtain a level a test that rejects Ho if Уп(X — во) VП(х — во) <21-a/2 21-a/2 or о Q2(1pt): Is the two-sided test derived in 1) an uniformly most powerful test? If not, briefly state your reasons Q3 (1pt): Note that the test...