Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-25T09:14:39.828Z Has data issue: false hasContentIssue false
  • English
  • Français

Further generalizations of Neumann's integral

Published online by Cambridge University Press:  09 April 2009

W. Pye
W. Pye
Affiliation:
Secondary Teachers' College and University of MelbourneVictoria, 3052, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A generalization of Neumann's integral connecting the two kinds of Legendre function is obtained. It contains an extra parameter which is not a function of the parameters of the Legendre functions, unlike all previous extensions of the original formula. These extensions are shown to be particular cases of the new generalization and some further particular cases are also indicated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 368 - 374
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Copson, E. T., Theory of Functions of a Complex Variable (Oxford, 1935).Google Scholar
[2]Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F., Higher Transcendental Functions, Vol. I (McGraw-Hill, New York, 1953).Google Scholar
[3]Gormley, P. G., ‘A Generalization of Neumann's Formula for Qn (z)’, J. London Math. Soc. 9 (1934), 149–152.CrossRefGoogle Scholar
[4]Love, E. R., ‘Franz Neumann's Integral of 1848’, Proc. Camb. Phil. Soc. 61, (1965), 445–456.CrossRefGoogle Scholar
[5]Robin, L., Fonctions sphériques de Legendre et fonctions sphériodales, Vol. I (Gauthier-Villars, Paris, 1957).Google Scholar
[6]Robin, L., Fonctions sphériques de Legendre et fonctions sphériodales, Vol. II (Gauthier-Villars, Paris 1958).Google Scholar
[7]Wrinch, Dorothy, ‘On Some Integrals involving Legendre Polynomials’. Phil. Mag. 7 (10) (1930), 1037–1043.CrossRefGoogle Scholar