$p$-arclength of the $q$-circle

By Peter Lindqvist, J. Peetre. 2003

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A new form of the generalized complete elliptic integrals (2014, methodology): “See [9, 10, 14, 16, 18, 22, 23, 24, 25, 28] for general properties as functions; [13, 14, 15, 22, 26, 29] for applications to differential equations involving p-Laplacian; [5, 10, 11, 16, 17, 22, 30] for basis properties for sequences of these functions.”
Inequalities for generalized trigonometric and hyperbolic functions with one parameter (2020, methodology): “For example, sin ∗ p and cos ∗ p are applied in the parametrization of so-called p -circle by Lindqvist and Peetre in [49], in which the authors proved that the area closed by the p -circle is π ∗ p R 2 , and the q -length ( l q metric) of p -circle is 2 π ∗ p R .”
Inequalities for the generalized trigonometric and hyperbolic functions (2012, background): “In particular, the reader is referred to [10–13].”