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 function
A 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
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.