The temperature field inside a "truncated" wedge is investigated.
For this purpose the two dimensional Green's function of the
heat equation for this domain is established. Further applications of
these results center around a problem of heat conduction investigated
by Lebedev.
The generalized Hankel transforms are studied in the
first part of this thesis; these include the Watson transforms
as a special case. For the validity of the reciprocal
relations, a necessary and sufficient condition on
the kernel is proved. The proof involves first changing
the variables so that all the...
A large number of results concerning the sums of certain
infinite series involving Legendre functions (including
conical functions) are derived. The generating
principle chosen here is based upon the application of
Integral transforms of the Fourier, Hankel and Meijer type
of finite and infinite character. This particular choice
leads to...
The electromagnetic field produced by a line current oriented
parallel to the edges of two perfectly conducting parallel half
planes is considered. Maxwell's equations reduce to a single wave
equation involving only one component of the electric field. Moreover
the value of the field is zero on the two half...
The electromagnetic field in a cone of arbitrary slant
height with a symmetrically placed time harmonic ring source is
studied. Through the use of the modified Helmholtz equation as
an intermediate, we obtain the solution of the semi-infinite
cone directly from the finite cone. To demonstrate the need
for the...
Application of a Mellin transform to a series which
represents a generalization of the Lerch zeta function
yields a transformation series. One obtains the asymptotic
behavior of the series, together with some associated
expansions and limit relations and moreover,a
specialization of parameters yields several classical
results.