R. Barakat, J. Opt. Soc. Am. 54, 920 (1964).
The area under τ(x), which is the total energy, equals unity.
M. Born and E. Wolf, Princi ples of Optics (Pergamon Press, Inc., London 1959), pp. 369, 484.
G. Toraldo di Francia, J. Opt. Soc. Am. 45, 497 (1955).
See Ref. 1.
M. Born and E. Wolf, Ref. 3, p. 483.
M. Born and E. Wolf, Ref. 3, p. 752.
This formula is due to R. Barakat (private communication).
E. C. Titchmarsh, The Theory of Functions (Oxford University Press, New York, 1939) 2nd ed., p. 434.
G. H. Hardy, Divergent Series (Oxford University Press, New York, 1949).
G. H. Hardy, Ref. 10, p. 101.
R. Barakat and A. Houston, J. Opt. Soc. Am. 53, 1244 (1963).
The first two expressions in (26) are obtained by summing the complex exponential, einu, according to the (C,1) definition. The remaining relationships in (26) can be found in R. Courant, Differential and Integral Calculus (Blackie & Son, Ltd., London and Glasgow, 1958), Vol. I, p. 446.
R. Barakat and A. Houston, J. Opt. Soc. Am. 54, 768 (1964).
It is easily seen that (28) gives the values T1 (0) =, and T1 (½∊) =0.