Hurwitz continued fractions with confluent hypergeometric functions

Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions ₀ F1(;c;z). In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions. This research was supported in part by the Grant-in-Aid for Scientific research (C) (No. 18540006), the Japan Society for the Promotion of Science.