| Popis: |
This chapter presents the generalized hypergeometric function p F q and the G -function. The G -function is significant as numerous special functions appearing in applied mathematics are special cases or are closely related. Thus, a result involving a G -function becomes a master or a key formula from which a very large number of results can be deduced for Bessel functions, Legendre functions, confluent hypergeometric functions, etc., their combinations and other related functions. The p F q is symmetric in its numerator parameters, and likewise in its denominator parameters. If a numerator parameter and a denominator parameter coalesce, then omit the parameter, whence the p F q becomes a p-1 F q-1 . The p F q series terminates and, therefore, is a polynomial if a numerator parameter is a negative integer or zero, provided that no denominator parameter is a negative integer or zero. |
