Some Infinite Series Involving Sonine's Polynomial

In general we can have two types of infinite series involving the polynomial:

Σ a_rT^r_m(x)                                         (A)

and

Σ b_rT_rⁿ(x)                                          (B).

Series of the type (A) have been discussed extensively from time to time by various authors, but very little is known about series of the type (B).