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
where j = 1,...,p, l = 1,...,m, and [[phi].sub.i] are real
meromorphic functions.
Among the topics are the Gopakumar-Ooguri-Vafa correspondence for Clifford-Klein 3-manifolds, the hybrid Landau-Ginzburg models of Calabi-Yau complete intersections, the quantization of spectral curves for
meromorphic Higgs bundles through topological recursion, graph sums in the remodeling conjecture, airy structures and the symplectic geometry of topological recursion, and quantum curves for simple Hurwitz numbers of an arbitrary base curve.
The last term on the right of (10) is obviously a
meromorphic function with simple poles at z = 0,1 and [z.sub.k].
The integrand of the integral on the left-hand side of (61) is
meromorphic in the region [absolute value of (z)] > 1 having there only simple poles at z = [z.sub.n], n = 1, ..., 2J-1 with residues ln [??](1/[z.sub.n]).
In the present paper, making use of the integral operator [W.sub.s,b]f(z) involving the Hurwitz-Lerch Zeta function, we have derived several third-order differential subordination and differential superordination consequences of
meromorphic functions in the punctured unit disk.
the ring of proper and stable rational functions [R.sub.PS], the ring of polynomials [R.sub.P] or the ring of proper and stable
meromorphic functions [R.sub.MS].
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.
In this paper, a
meromorphic function means a function that is
meromorphic in the whole complex plane C.
and has the
meromorphic continuation to the whole complex plane with unique simple pole at the point s = 1 with residue 1.
We also consider the class [SIGMA] of
meromorphic univalent functions in D* := {z [member of] [??] : |z| > 1} having a simple pole at infinity with residue 1.