Journal article
Spherical curves and quadratic relationships for special functions
Journal of the Australian Mathematical Society. Series B, Applied mathematics, v 27(1), pp 111-124
Jul 1985
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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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Details
- Title
- Spherical curves and quadratic relationships for special functions
- Creators
- Even Mehlum - Central Institute for Industrial Research, Oslo, Norway.Jet Wimp - Drexel University
- Publication Details
- Journal of the Australian Mathematical Society. Series B, Applied mathematics, v 27(1), pp 111-124
- Publisher
- Cambridge University Press
- Number of pages
- 14
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1985AKA8200007
- Other Identifier
- 991019312376804721
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- Collaboration types
- International collaboration
- Web of Science research areas
- Mathematics, Applied