Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-12T06:57:28.659Z Has data issue: false hasContentIssue false
  • English
  • Français

The solution of dual cosine series by the use of orthogonality relations

Published online by Cambridge University Press:  20 January 2009

B. Noble  and
J. R. Whiteman
B. Noble
Affiliation:
Mathematics Research Center, University of Wisconsin
J. R. Whiteman
Affiliation:
Mathematics Research Center, University of Wisconsin
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.

In this paper expressions are derived for the unknown coefficients in the dual cosine series:

where α is a given constant, and f1(x) and f2(x) are prescribed functions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 47 - 51
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

(1) Cooke, J. C., Note on a pair of dual trigonometrical series, Glasgow Math. J. 9 (1968), 30–35.CrossRefGoogle Scholar
(2) Erdélyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693.CrossRefGoogle Scholar
(3) Magnus, W. and Oberhettinger, F., Special Functions of Mathematical Physics (Chelsea, New York, 1949).Google Scholar
(4) Noble, B., Some dual series equations involving Jacobi polynomials, Proc.Cambridge Philos. Soc. 59 (1963), 363–371.CrossRefGoogle Scholar
(5) Noble, B. and Whiteman, J. R., Solution of dual trigonometrical series using orthogonality relations (Mathematics Research Center, Technical Summary Report #890, Madison, 1968).Google Scholar
(6) Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory(North Holland, Amsterdam, 1966).Google Scholar
(7) Srtvastav, R. P., Dual series relations—III. Dual relations involving trigono- metrical series, Proc. Roy. Soc. Edinburgh, Sect. A 66 (1964), 173–184.Google Scholar
(8) Tranter, C. J., An improved method for dual trigonometrical series, Proc. Glasgow Math. Assoc. 6 (1964), 136–140.CrossRefGoogle Scholar