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

q 2 pys
2.13. In a cubic crystal, (hkl), (101), and (011) belong to a zone. This (hkl) plane also lies in another zone containing (213) and (211). What is (hkl) if the angle between (hkl) and (101) is 19.01°?
A student from Isabela State University launched a rocket that has a payload of atmospheric sensors. The payload contains an altimeter and a digital barometer. From one of the University’s class room where they built a data receiving area, the altimeter sends 10 values of altitude, 5600 ft, 5000 ft, 4600ft, 4100 ft, 3800 ft, 3500 ft, 3150 ft, 2900 ft, 2300 ft, and 1300 ft. But the data of the barometer wasn’t sent because of a circuit anomaly. But the programmer assured that it will be recorded in the memory inside the payload’s microcontroller. Assuming the air density to be 1.18 ??/?3, what pressure we should expect depending on the data sent by the altimeter?
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
Give examples of three physical quantities that are having dimensions [ M L-1 T-2]
2) Rewrite the following expression in proper scientific notation as in the example on page 1. Note that here you also have to take care of the number of significant digits. ((140.88)(18.775)(60110)(7.76))/((0.00024)(401×10^8)(88.0))= 3) Solve the above expression using your calculator. Round your answer to the appropriate number of significant digits. Explain how you round it.
= U is for Uranium. Natural uranium consists of 235U (percent abundance P₁ = 0.7300%, A₁ = 3.12 x 10-¹7 [s-¹]) and 233U (percent abundance P₂ = 99.27%, 2₂ = 4.92 × 10-¹8 [s-¹]). Consider the time when Earth was formed 4.5 billion years ago. Setup the time dependence of percent abundance of the two uranium isotopes. Use №₁ and N₂ as current particle count of the isotopes (use №₁,0 and N₂,0 for the initial particle count back when Earth was formed) Then, Compute for the initial percent abundance of each uranium isotopes when the Earth was formed.
solve this and provide step by step your calculation
I submitted this before but I don't think the answer was 100% correct. Can someone write it out in full on the answers and how they were achieved?
vast CMSCT - Module 22 34 Read the measurement on the U.S. Vernier caliper. Express your answers to three (3) decimal places. 0 5 7 8 9 20 Main scale reading: Vernier scale reading: Final reading: 10 30 15 20 0 1 2 3 4 5 6 7 8 9 10 25 0.001 in. 1 5 6 7 8 9 1 2 3 4 5 6 7 8 9 2 50 40 60 70 0.05 mm
Please send me answer of this question immediately and i will give you like sure sir
2. 3. 4. Show a comparison of the masses of the three subatomic particles using a bar graph. Refer to Figure 2 in the next page, assuming that the first bar represents the mass of the proton; draw the bars to represent the masses of the neutron and the electron. Take note that the masses are expressed in the -28 exponent. This time, using a pie chart, show the proportion of the masses of the subatomic particles for an atom composed of only 1 proton, 1 neutron and 1 electron. A seesaw can show a comparison between two masses of an object. A seesaw goes up and down depending on the mass it carries on each side. Q4. How does the mass of the neutron compare with the mass of the proton? Using circles to represent the particles show the comparison by drawing a seesaw with the particles on it. 5. Q5. How many electrons should be placed on one side of the seesaw to balance it if the other side has 1 proton on it, like the one shown below? Write the number on the space provided in the…