Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-28T09:15:56.780Z Has data issue: false hasContentIssue false
  • English
  • Français

On triple trigonometrical equations

Published online by Cambridge University Press:  18 May 2009

B. M. Singh
B. M. Singh
Affiliation:
Samrat Ashok Technological Institute, Vidisha, Madhya Pradesh, India
Rights & Permissions [Opens in a new window]

Extract

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.

An exact solution of triple trigonometrical equations is obtained by using the finiteHilbert transform. The solution of these equations is used to solve a two-dimensional electrostatic problem. The problem of determining the electrostatic potential due to two parallel coplanar strips of equal length, charged to equal and opposite potentials, each parallel to and equidistant from an earthed strip, is considered. Both the charged strips lie along the x-axis and they are equally spaced with respect to the y-axis. Finally the expression for the surface charge density (per unit depth) of the strip is derived

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 174 - 178
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Babloian, A. A., Solution of certain dual integral equations, Prikl. Mat. Mekh. 22 (1964), 1015–1023.Google Scholar
2.Tricomi, F. G., On the finite Hilbert transformation, Quart. J. Math. Oxford Ser. (2) 2 (1951), 199–211.CrossRefGoogle Scholar
3.Tricomi, F. G., Integral equations (New York, 1957).Google Scholar
4.Tranter, C. J., Some triple integral equations, Proc. Glasgow Math. Assoc. 4 (1960), 200–203.CrossRefGoogle Scholar
5.Sneddon, I. N., Mixed boundary value problems in potential theory (Amsterdam, 1966).Google Scholar
6.Gradsheyn, I. S. and Ryzhik, I. M., Tables of integrals, series and products (Academic Press, 1965).Google Scholar
7.Srivastava, K. N. and Lowengrub, M., Finite Hilberttransform technique for triple integral equations with trigonometric kernels, Proc. Roy. Soc. Edinburgh Sect. A 68 (1970), 309–321.Google Scholar
8.Srivastava, K. N., On some triple integral equations involving Legendre functions of imaginary argument, Journal of M.A.C.T. 1 (1968), 54–67.Google Scholar