Learning Materials
Features
Discover
Chapter 12: Q8-1P (page 562)
Find the norm of each of the following functions on the given interval and state the normalized function.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Using (17.3) and (15.1) to (15.5), find the recursion relations for . In particular, show that .
Use the table above and the definitions in Section 17 to find approximate formulas for large x for :
The equation for the associated Legendre functions (and for Legendre functions when m=0) usually arises in the form (see, for example, Chapter 13, Section 7) 1/sinθ d/dθ (sinθ dy/dθ)+[l (l+1)-m2/sin2θ] y=0.
Make the change of variable x=cosθ, and obtain (10.1):
(1-x2) y"-2xy'+[l (l+1) -m2/1-x2] y=0
For Problems 1 to 4, find one (simple) solution of each differential equation by series, and then find the second solution by the "reduction of order" method, Chapter 8, Section .
To study the approximations in the table, a computer plot on the same axes the given function together with its small x approximation and its asymptotic approximation. Use an interval large enough to show the asymptotic approximation agreeing with the function for large x. If the small x approximation is not clear, plot it alone with the function over a small interval
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App