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A Trivial Extension of Saxena’s I-Function

Saxena, V. P.
National Academy science letters 2015 v.38 no.3 pp. 243-245
equations, geometry, mathematical theory
In this communication it is shown that the so called generalization of Saxena’s I-function, named as Aleph function, is nothing but another form of the I-function which is the subsequent generalization of Fox’s H-function and last generalization of Hypergeometric functions. This implies that the said generalization in the form of Aleph function is redundant. Later on, other authors have also studied this so called generalization of I-function. All such studies are in fact, studies of the earlier function (I-function) unless or otherwise it indicates some new properties of both I-function and Aleph function. This later function does not reveal any significant change either in the definition or conditions of existence. The denominator of the complex integrand under contour integral, which is in the form of a finite summation, has an additional constant coefficient in each term. This coefficient can be expressed as a quotient of gamma functions. Hence the same can be absorbed in the definition of I-function.