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A question from (mathematical physics - Couchy integral
formula)
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Show that
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A question from (mathematical physics - Couchy integral
formula)
c) The Rodrigues formula...
ECE question
Prove the recurrence relation
xPn(x) = n + 1
2n + 1
Pn+1(x) + n
2n + 1
Pn−1(x),
and evaluate the following integral using the orthogonal property of Legendre polynomials
Z 1
−1
xPn(x)Pn−1(x)dx
From Arfken. how to get from equation 13.59 to equation 13.60 the new contour enclosing the point s (for derivatives),...
From Arfken.
how to get from equation 13.59 to equation 13.60
the new contour enclosing the point s (for derivatives), in the s-plane. By Cauchy's integral formula nrd/T(x"e-*)| | Ln(x) = (integral n) (13.59) giving Rodrigues' formula for Laguerre polynomials. From these representations of Ln(x) we find the series form (for integral n) n2(n - 1)- n-2 2! (13.60)
the new contour enclosing the point s (for derivatives), in the s-plane. By Cauchy's integral formula nrd/T(x"e-*)| | Ln(x) = (integral...
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 functi...
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...
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.
Show that integral dz/(z-1-i)n+1 =0, if n does not equal 0 and 2 pi i if n = 0 for C the boundary...
Show that integral dz/(z-1-i)n+1 =0, if n does not equal 0 and 2 pi i if n = 0 for C the boundary of the square 0<=x<=2, 0<=y<=2, taken counterclockwise. [Hint: Use the fact that contours can be deformed into simpler shapes (like a circle) as long as the integrand is analytic in the region between them. After picking a simpler contour, integrate using parametrization.]
Question 6 (10 marks) In this question you are asked to produce a proof of the...
Question 6 (10 marks) In this question you are asked to produce a proof of the following identity: $(2) = (1) n=1 (a) Let N > 1 be a natural number. Evaluate the integral 1 Cos(12) IN = -dz, 2ni lov z2 sin(T2) where Cn is the positively oriented, square contour shown in Figure 1. (N+ 5)(-1+i) (N + 1)(1+i) (N+ 3)(-1 - i) (N + 1)(1 - ) Figure 1: The contour Cn. In your working, the following limit...
IN C 4) Convert the following mathematical formula to a C code, where Z, a, b...
IN C
4) Convert the following mathematical formula to a C code, where Z, a, b and c are doubles (You do not need to write the whole program, just write the code fragment) Z-a + sqrt(b+3 5-2)/(c 5)*3 mod 5 5) Write a program that prompts the user to enter an integer number (N) and then displays the following (2N+1)-by-(2N+1) pattern like the one below Enter a number: 4
QUESTION 2. PLEASE USE COMPUTER WRITING SO I CAN READ IT 52 Complex Analysis Exercises (1)...
QUESTION 2.
PLEASE USE COMPUTER WRITING SO I CAN READ IT
52 Complex Analysis Exercises (1) Does the function w = f(2) za have an antiderivative on C? Explain your answer. (2) Is (z dz = 0 for every closed contour I in C? How do you reconcile your conclusion with Cauchy's integral theorem? (3) Compute fc Log(x+3) dz, where is the circle with radius 2. cente at the origin and oriented once in the counterclockwise direction. (4) Let I...
1. Use an antiderivative to show that for every contour C extending from a point zi...
1. Use an antiderivative to show that for every contour C extending from a point zi to a point z2 2 dz= n+1 (n =0, 1,2,...). n+ 1
the previous hw question and answer 1. Consider the integral from question 2 of the previous...
the previous hw question and answer
1. Consider the integral from question 2 of the previous homework assignment: too sin ma dx, and assume that both m and a are positive real numbers. By using an indented contour, evaluate this integral fully. You are allowed to resubmit material submitted as part of the previous assignment if you wish.] 2. (30 marks] Evaluate the following integrals: too sin ma x(x2 + a2) dar, m, a real, a +0. rt eike dx,...
From Arfken.
how to get from equation 13.59 to equation 13.60
the new contour enclosing the point s (for derivatives), in the s-plane. By Cauchy's integral formula nrd/T(x"e-*)| | Ln(x) = (integral n) (13.59) giving Rodrigues' formula for Laguerre polynomials. From these representations of Ln(x) we find the series form (for integral n) n2(n - 1)- n-2 2! (13.60)
the new contour enclosing the point s (for derivatives), in the s-plane. By Cauchy's integral formula nrd/T(x"e-*)| | Ln(x) = (integral...
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.
Question 6 (10 marks) In this question you are asked to produce a proof of the following identity: $(2) = (1) n=1 (a) Let N > 1 be a natural number. Evaluate the integral 1 Cos(12) IN = -dz, 2ni lov z2 sin(T2) where Cn is the positively oriented, square contour shown in Figure 1. (N+ 5)(-1+i) (N + 1)(1+i) (N+ 3)(-1 - i) (N + 1)(1 - ) Figure 1: The contour Cn. In your working, the following limit...
IN C
4) Convert the following mathematical formula to a C code, where Z, a, b and c are doubles (You do not need to write the whole program, just write the code fragment) Z-a + sqrt(b+3 5-2)/(c 5)*3 mod 5 5) Write a program that prompts the user to enter an integer number (N) and then displays the following (2N+1)-by-(2N+1) pattern like the one below Enter a number: 4
QUESTION 2.
PLEASE USE COMPUTER WRITING SO I CAN READ IT
52 Complex Analysis Exercises (1) Does the function w = f(2) za have an antiderivative on C? Explain your answer. (2) Is (z dz = 0 for every closed contour I in C? How do you reconcile your conclusion with Cauchy's integral theorem? (3) Compute fc Log(x+3) dz, where is the circle with radius 2. cente at the origin and oriented once in the counterclockwise direction. (4) Let I...
1. Use an antiderivative to show that for every contour C extending from a point zi to a point z2 2 dz= n+1 (n =0, 1,2,...). n+ 1
the previous hw question and answer
1. Consider the integral from question 2 of the previous homework assignment: too sin ma dx, and assume that both m and a are positive real numbers. By using an indented contour, evaluate this integral fully. You are allowed to resubmit material submitted as part of the previous assignment if you wish.] 2. (30 marks] Evaluate the following integrals: too sin ma x(x2 + a2) dar, m, a real, a +0. rt eike dx,...
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