Complete the proof of Lemma 5.1.2(b) by showing that if andare one-to-one correspondences, then givenby f (a, b) = (h(a), g(b)) is a one-to-one correspondence.

S343 Section 5.6 Notes- Series Solutions Near a Regular Singular Point (Part 2) 12-6-16 2 ′′ ′ 2 Consider general problem of finding solution of = + + = 0, where = ∑=0 and =) ∑ =0 o Both series converge in < for > 0 2 ′′ ′ o 0= 0 is regular singular point; corresponding Euler equation is 0 + 0+ = 0 o Seek solution for > 0 of form = , = ∑∞ = ∑∞ +