 12.1: xy = xy + y
 12.2: y = 3x2 y
 12.3: xy = y
 12.4: y = 4y
 12.5: y = y
 12.6: y 2y + y = 0
 12.7: x2 y 3xy + 3y = 0
 12.8: (x2 + 2x)y 2(x + 1)y + 2y = 0
 12.9: (x2 + 1)y 2xy + 2y = 0
 12.10: y 4xy + (4x2 2)y = 0
 12.11: x x3
 12.12: 7x4 3x + 1
 12.13: x5
 12.14: Show that any polynomial of degree n can be written as a linear com...
 12.15: Expand the potential V = K/d in (5.11) in the following way in orde...
 12.16: Prove the least squares approximation property of Legendre polynomi...
 12.17: xy + y + 9xy = 0
 12.18: y2(x)
 12.19: Computer plot on the same axes several Ip(x) functions together wit...
 12.20: As in 19, study the Kp(x) functions. It is interesting to note (see...
 12.21: Verify that the polynomials Lk n(x) in (22.25) satisfy (22.26). Hin...
 12.22: Verify that the polynomials given by (22.27) are the same as the Lk...
 12.23: Verify the recursion relation relations (22.28) as follows: (a) In ...
 12.24: Show that the functions Lk n(x) are orthogonal on (0,) with respect...
 12.25: Evaluate the normalization integrals (22.29) and (22.30). Hints: Us...
 12.26: Solve the following eigenvalue problem (see end of Section 2 and 11...
 12.27: The functions which are of interest in the theory of the hydrogen a...
 12.28: Repeat for l = 0, n = 1, 2, 3.
 12.29: Show that Rp = p x D and Lp = p x + D where D = d/dx, are raising a...
 12.30: Find raising and lowering operators (see 29) for spherical Bessel f...
Solutions for Chapter 12: Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions
Full solutions for Mathematical Methods in the Physical Sciences  3rd Edition
ISBN: 9780471198260
Solutions for Chapter 12: Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions
Get Full SolutionsChapter 12: Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions includes 30 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Methods in the Physical Sciences, edition: 3. Since 30 problems in chapter 12: Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions have been answered, more than 7260 students have viewed full stepbystep solutions from this chapter. Mathematical Methods in the Physical Sciences was written by and is associated to the ISBN: 9780471198260.

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