3 citations · 3 across the 4 of their papers we have counts for
7 papers
A Class of Fractions adding how Pupils wish
Martin Himmel
Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.
Cauchy Pairs
Martin Himmel
The notion of pairable functions is introduced and some of its properties are developed. In this connection the famous Euler identity is interpreted as a property of certain pairab…
Pendants to the Euler Beta function
Martin Himmel
Motivated by the integral representation of the Euler Beta function, we introduce its Cauchy siblings and investigate some of their properties. Two of these newly introduced functi…
The logarithmic Cauchy quotient mean
Martin Himmel, Janusz Matkowski
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
Homogeneous Beta-type functions
Martin Himmel, Janusz Matkowski
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reform…
Directional convexity and characterizations of Beta and Gamma functions
Martin Himmel, Janu sz Matkowski
The logarithmic convexity of restrictions of the Beta functions to rays parallel to the main diagonal and the functional equation \[ ϕ\left( x+1\right) =\frac{x\left( x+k\right) }{…