A Holomorphic Function is a Complex-Valued Function of One or More Complex Variables That is Complex-Differentiable in a Neighborhood of Each Point in a Domain, in Complex-Coordinate Space (Cn).

The Existence of a Complex Derivative in a Neighborhood is a Very Strong Condition: it Implies That a Holomorphic Function is Infinitely Differentiable & Locally Equal to Its Own Taylor Series Expansions. Holomorphic Functions Are The Central Objects of Study in Complex Analysis.

Vector-Valued Holomorphic Functions Defined in The Complex Plane:

A Tangible Step in Extending The Theory of Holomorphic Functions Beyond One Complex Dimension is to Take a Trip Into This Visceral Realm, With a Bit of Synesthetic Pleasure. The Following is a Snippet From One of Producer M3TA's Live Visual Performances. Allow The High-Dimensional Cymatic Geometries & Musical Vibes to Transport You to a Whole New Plane of Existence.

Musical Remix by: Smigonaut (Electric Forces by Voljum).

Minted With Love,

M3TA