The foundational aspects of Gauss's work on the hypergeometric, factorial and digamma functions

Details The foundational aspects of Gauss's work on the hypergeometric, factorial and digamma functions The foundational aspects of Gauss's work on the hypergeometric, factorial and digamma functions

Sep 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007ahes...61..457f&link_type=abstract

Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 61, No. 5, p. 457 - 518 (2008)

Statistics

Methodology

History Of Science

Scientific paper

In his writings about hypergeometric functions Gauss succeeded in moving beyond the restricted domain of eighteenth-century functions by changing several basic notions of analysis. He rejected formal methodology and the traditional notions of functions, complex numbers, infinite numbers, integration, and the sum of a series. Indeed, he thought that analysis derived from a few, intuitively given notions by means of other well-defined concepts which were reducible to intuitive ones. Gauss considered functions to be relations between continuous variable quantities while he regarded integration and summation as appropriate operations with limits. He also regarded infinite and infinitesimal numbers as a façon de parler and used inequalities in order to prove the existence of certain limits. He took complex numbers to have the same legitimacy as real quantities. However, Gauss's continuum was linked to a revised form of the eighteenth-century notion of continuous quantity: it was not reducible to a set of numbers but was immediately given.

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