Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Complexdifferentiable on an open set around every point in its domain.
from The Century Dictionary and Cyclopedia
 Exhibiting holohedral symmetry.
 In mathematics, having the form of an entire function.
 Noting a function of a complex variable which is continuous, onevalued, and has a derived function when the variable moves in a certain region of the plane: so called to indicate that it is like an integer function for which this property holds throughout the entire plane.
Etymologies
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Examples

Section 33.10 explains how positive/negative frequency splitting along with "holomorphic first sheaf cohomology" plays "a direct role in generating deformations of twistor space."

We start by looking at the class of holomorphic functions — essentially polynomials of infinite degree.
Wolfram Blog : Mathematica 7, Johannes Kepler, and Transcendental Roots

A holomorphic function will often have infinitely many roots.
Wolfram Blog : Mathematica 7, Johannes Kepler, and Transcendental Roots

The action of a real semisimple lie group on a complex flag manifold, II: Unitary representations on partially holomorphic cohomology spaces by Joseph Albert Wolf

Genealogical concordance and recombination analyses confirm the existence of two genetically isolated agamospecies including T. harzianum sensu stricto and two hypothetical holomorphic species related to but different from H. lixii.

Questions: are both sides of the OSV welldefined, is it true everywhere, what do the holomorphic anomalies do, is it consistent with elmg. dualities, consistent nonperturbatively?

So the normal BCOV holomorphic anomaly  one for closed strings  must be extended to the open string.

He must extend the holomorphic anomaly equation first.

The sum obeys the extended holomorphic anomaly equation.

BCOV 1993 shows that Bmodel amplitudes depend on CS moduli nonholomorphically: that's the holomorphic anomaly, arising from the boundary of the Riemann surface moduli space.
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