  This paper studies eight families of infinite series involving hyperbolic
functions. Under some conditions, these series are linear combinations of
derivatives of Eisenstein series. The paper gives a systematic method for
computing the values of these series at CM points. The approach utilizes
complex multiplication theory, the structure of the rings of modular forms and
quasimodular forms, and certain differential operators defined on these rings.
This paper also expresses the generalized reciprocal sums of Fibonacci numbers
as the special values of the series mentioned above. Thus it gives some
algebraic independence results about the generalized reciprocal sums of
Fibonacci numbers.
