Abstract: Stieltjes
transforms refer to integrals with integrand ds(t)/(t
+ z),the
range from zero to ¥.
Other continued fractions are related to this
form and appear in the form Second
order continued fractions relate to a definite
integral with integrand ds(t)/(t
+ z1)
(t +
z2).The
Fibonacci c.f. is or
with
z
= 1.The
2nd order c.f., relates to Based
on these 2nd order c.f.s, results are derived
for properties of Fibonacci numbers and the
squares of Fibonacci numbers.
Keywords and phrases: recurrence relations, S-fractions, Stieltjes integrals, Stieltjes moment problem.
