An expression of certain known functions as generalized hypergeometric functions

It has long been known that many functions (e. g. y the logarithm and the Legendre functions) are particular cases of the hypergeometric function, and that other functions (e. g., the exponential function and the Bessel functions) are limiting cases of the hypergeometric function. The object of the present paper is to show that the latter class of functions is much larger than has hitherto been supposed ; that, in fact, it includes (in addition to those functions already known to belong to it) the following five types of functions, namely :