0
votes
1answer
207 views

recurrence relation of integral

Consider the integral defined by $$\displaystyle{ I_k( \phi) = \int_0^{\pi} \frac{ \cos(k\theta) - \cos( k \phi) }{ \cos \theta - \cos\phi} d \theta} $$ (a) Show that $I_k( \phi) $ satisfies the ...
4
votes
1answer
104 views

How can we approximate $\sum_{j=0}^n{\sum_{k=0}^j{c^j k^{1/2}}}$ by integrals?

"Difference Equations" by Walter G. Kelley and Allan C. Peterson, 2nd Edition, gives an example on how to approximate $\sum_{k=1}^n{k^{1/2}}$ using integrals and Bernoulli numbers. I'm interested in ...