On totally positive sequences and functions |
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Authors: | Michael I Ganzburg |
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Institution: | Department of Mathematics, Hampton University, Hampton, VA 23668, USA |
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Abstract: | Let a>0 be a fixed number. A function f:R→R is said to be a-shift-generating (a-SG) if for every x∈R, is a totally positive sequence and it does not coincide with a sequence of the form , where A?0 and λ>0. In this paper, we describe all a-SG functions and obtain a new characterization of totally positive functions in the terms of a-SG functions. In addition, using characteristic properties of a-SG functions, we generalize the famous Jacobian identity in theory of elliptic functions. |
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Keywords: | Totally positive sequences Totally positive functions Jacobian identity |
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