By construction [S.sub.r](s) is a
meromorphic function in s [member of] C and when r [greater than or equal to] 2 it has the following expression
Each element of [??] is the image of a
meromorphic function under the map [e.sub.[SIGMA]].
We say that a
meromorphic function [zeta] belongs to the class W if [zeta] is an elliptic function, or a rational function of z, or a rational function of [e.sup.[mu]z], [mu] [member of] C.
In this paper, a
meromorphic function means a function that is meromorphic in the whole complex plane C.
Due to the complication to study the distribution of public zero of two L-functions, researchers take up study of the relationship of an L-function and a
meromorphic function. Since L-function itself can be analytically continued as a
meromorphic function in the whole complex plane, therefore, L-functions will be taken as special
meromorphic functions, with the help of Nevanlinna's value distribution theory, in order to study the uniqueness of L-functions.
Key words and phrases :
Meromorphic function, Concave function, Starlike function, Dirichlet finite integral, Integral mean.
Notation of the pole point is connected with
meromorphic functionA
meromorphic function w(z) means that w(z) is holomorphic in the complex plane C except for poles.
Observe that [[zeta].sub.E,q](s) is a
meromorphic function on C.
Let f be a transcendental
meromorphic function in C, all of whose zeros have multiplicity at least 3.
Denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the set of poles of the
meromorphic function F([alpha]) and by p([zeta]) the order of the pole [zeta] for [zeta] [member of] P.
Numerical results, including reconstruction of a
meromorphic function and the induced current density in discontinuous material distributions, are shown in Section 3.