Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators

Tiago Jose Arruda; Rodrigo Silva Gonzalez; Cesar Augusto Sangaletti Tercariol; Alexandre Souto Martinez

doi:10.1016/j.physleta.2007.12.020

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arXiv · 0709.0018

Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators

Tiago Jose Arruda·Rodrigo Silva Gonzalez·Cesar Augusto Sangaletti Tercariol·Alexandre Souto Martinez

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Abstract

One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on several values of a variable are obtained here. Applications of the above formalism are considered.

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Tiago Jose Arruda, Rodrigo Silva Gonzalez, Cesar Augusto Sangaletti Tercariol, Alexandre Souto Martinez. 2007-08-31. Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators. https://doi.org/10.1016/j.physleta.2007.12.020

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