Hypergeometrical

Part of speech: adjective

Definitions

1. Relating to a hypergeometric function, a special mathematical function arising in series and differential equations, or to the probability distribution built on it
2. Describing the mathematical functions and probability models based on drawing items without replacement from a finite population and counting successes
3. Pertaining to the hypergeometric family of functions or distributions used in statistics, combinatorics and the solution of certain differential equations

Etymology: "Hypergeometrical" is simply "hyper-" attached to "geometrical," and the arithmetic of the prefix is the interesting part. "Hyper-" comes from Greek "hyper," meaning "over," "beyond," or "above," and in mathematics it marks a generalisation that goes beyond the ordinary case. The base word "geometrical" traces back through Latin "geometricus" to Greek "geōmetrikos," from "geōmetria," literally "earth-measuring." Put together, the compound describes functions that extend the familiar geometric series, the sequence where each term is a fixed multiple of the one before. The term belongs to technical mathematical vocabulary, used where the ordinary geometric pattern has been pushed into a broader family of functions. Its meaning is fixed by that mathematical use, so the word is best read as a precise technical coinage rather than a term with a dramatic history of shifting senses.