The summation of series involving the roots of certain transcendental equations having real roots is achieved by elementary considerations. The method is illustrated by several examples representative of those which may arise in applications. In addition to summing series, the method can be used to obtain the least positive root of the transcendental equation to any desired accuracy with but little computation.
REFERENCES
1.
Lord Rayleigh, Theory of Sound (Macmillan and Company, Ltd., London, 1894), Vol. I, p. 258.
2.
This is a sufficient condition but not necessary, as will be pointed out at the end of Example 4 in Sec. III.
3.
A method for calculation of these sums is given in Barnard and Child, Advanced Algebra (Macmillan and Company, Ltd., London, 1939), p. 48.
4.
E. C. Titchmarsh, The Theory of Functions (Oxford University Press, New York, 1939), second edition, p. 246.
5.
The results in this example may also be obtained by use of methods shown in the author’s paper,
J. Appl. Phys.
23
, 906
(1952
).
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© 1953 American Institute of Physics.
1953
American Institute of Physics
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