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The use of Riemann problems in solving a class of transcendental equations

Published online by Cambridge University Press:  24 October 2008

E. E. Burniston  and
C. E. Siewert
E. E. Burniston
Affiliation:
Departments of Mathematics and Nuclear Engineering, North Carolina State University, Raleigh, North Carolina 27607
C. E. Siewert
Affiliation:
Departments of Mathematics and Nuclear Engineering, North Carolina State University, Raleigh, North Carolina 27607
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Abstract

A method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 111 - 118
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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