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Spherical curves and quadratic relationships for special functions
Journal article   Open access

Spherical curves and quadratic relationships for special functions

Even Mehlum and Jet Wimp
Journal of the Australian Mathematical Society. Series B, Applied mathematics, v 27(1), pp 111-124
Jul 1985
url
https://doi.org/10.1017/s0334270000004793View
Published, Version of Record (VoR)Maybe Open Access (Publisher Bronze) Open

Abstract

We show that the position vector of any 3-space curve lying on a sphere satisfies a third-order linear (vector) differential equation whose coefficients involve a single arbitrary function A(s). By making various identifications of A(s), we are led to nonlinear identities for a number of higher transcendental functions: Bessel functions, Horn functions, generalized hypergeometric functions, etc. These can be considered natural geometrical generalizations of sin2t + cos2t = 1. We conclude with some applications to the theory of splines.

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Collaboration types
International collaboration
Web of Science research areas
Mathematics, Applied
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