1dnGiven the Rodriguez formula Pn(x) = 2n!(x²-1)", show that Pm (x) = (1-x²)m/² mm Pn(x)2″n! dx" 1)”,dmdxmis a solution of the associated Legendre eqn. (1 − x²)y" − 2xy' + [n(n + 1) − _m²/2]y = 0.Hint: show that the equation. can be obtained by differentiating the Legendre Equation(1 —-x²) z"x²)z" − 2xz' + n(n+1)z = 0m times w.r.t. x, followed by the substitution z = y(1-x²)-m/2.

We begin by differentiating the Legendre equation, (1-x^2) y'' - 2xy' + n(n+1) y = 0 m times with…

Given the Rodriguez formula P₁(x) = 2"n! dx" (x²-1)", show that Pm (x) = (1-x²)m/2 mm Pn(x) dm dam is a solution of the associated Legendre eqn. (1-x²)y" - 2xy' + [n(n + 1) — [m²]y = 0. Hint: show that the equation. can be obtained by differentiating the Legendre Equation (1-x²)z" - 2xz' + n(n+1)z = 0 m times w.r.t. x, followed by the substitution z = y(1-x²)-m/2.

Given the Rodriguez formula P₁(x) = 2"n! dx" (x²-1)", show that Pm (x) = (1-x²)m/2 mm Pn(x) dm dam is a solution of the associated Legendre eqn. (1-x²)y" - 2xy' + [n(n + 1) — [m²]y = 0. Hint: show that the equation. can be obtained by differentiating the Legendre Equation (1-x²)z" - 2xz' + n(n+1)z = 0 m times w.r.t. x, followed by the substitution z = y(1-x²)-m/2.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Given that L* = L,±iL, and L+Ym (0, 0) = NËYm÷1 (0, 0), where N = h/(e+1+m) (l = m), %3D show that, L+ + L- L+ - L- (a) L, = and L, 2 2i (b)L,Y10 (0, 6) = cY1 (0,6) + c„Y1-1 (0, 6) and find the constants e and c2. (c)Consider the function (0,6), which has the expansion 1 v (0, 6) = E amYım (0,9), where ao = 2v2, a1 = a-1 = 2. %3D m=-1 Show that (0, 0) is an eigenfunction of L, and find the corresponding eigenvalue.
7letA-Cam)e+ Com)-Cam)Rand B (4m) Î + Camdî (2m) R. A)(8m)î+ Ciamdî- Com) i B) (1am)î-Ciy m) ŷ-Caom) R C23 %3D Then À.B equals: Dwone of these
If a student measured the edge length of a cubic metal nine times as follows: 5.16, 5.29, 5.20, 5.08, 5.23, 5.36, 5.11, 5.28 and 5.12 cm. The student also measured the mass of the cube to be 380.5±0.5 g. Answer the following four questions 1.5/6 2. 3. 1. The sample standard deviation for the edge length of the cube is 0.09 cm 0.03 cm 0.05 cm 4. a. c. d. 0.12 cm e. 0.06 cm The best estimate for the edge length of the cube is a. 5.2033+0.0315 cm b. 5.2033+0.0944 cm c. 5.20+0.09 cm d. 5.20+0.06 cm 5.2010.03 cm The volume of the cubic metallic piece is a. 140.910.09 cm3 140.8+0.08 cm3 c. 14113 cm3. d. 140+2 cm3 e. 140+3 cm3 The density of the metal is a. 2.71±0.07 g/cm3 (b) 2.700±0.06 g/cm3 c. 2.700+0.005 g/cm3 d. 2.70±0.06 g/cm3 e. 2.70±0.05 g/cm3 t
q 2 pys
S Can 6 PAR к Торс K Unit K In x K Moti = Cop K Unit S Spee S Topo S Math Micr eb.kamihq.com/web/viewer.html?source-filepicker&document_identifier=137VZR5BZOVSAIMOA55WU555_CvJ9NacO + 100 P e Interpreting Graphs Answer the questions following the graphs on each side Dietance va. Time 2 7 10 11 12 13 14 Time in soconds 1. From 1 second to 2 seconds, how fast is the object traveling. (Take the difference in distance and divide it by the time in between the 2 distances) 2. Is the object going as fast between 9 and 12 seconds as it is between 1 and 4 seconds? How can you tell? 3. What is the motion of the object between 4 and 6 seconds? acer
Determine the range
-3 Find Y? -> (2d41)(d-m)! imo m e Pi (Cose) -3 Y3 cOn)= | e (2(3)+1)(3-(-3)! Pj (coS e) 4Y (3+¢3))!
An element makes up 0.0021% of the Earth's continental crust by mass. Express this in ppm (parts per million), to an appropriate number of significant figures
(in nm) is nano meters THz is Tera Hertz
State how many significant figures are proper in the results of the following calculations. (a) (36.842100) (265) (46.210) (2) (b) (5.9)² (c) (356.23 x 10-19) (3712)
A valid, but probably useless, dimensionless group is givenby (μT0g)/ (YLα) , where everything has its usual meaning,except α . What are the dimensions of α ?( a ) θL-1T-1 , ( b ) θL-1T-2 , ( c ) θML-1 , ( d ) θ-1LT-1 ,( e ) θLT-1
solve this and provide step by step your calculation