ETA (LETTER)

:''For other uses, see Eta.''

'Eta' (uppercase 'Η', lowercase 'η') is the seventh letter of the Greek alphabet. In the system of Greek numerals it has a value of 8. It was derived from the Phoenician letter Heth . Letters that arose from Eta include the Latin H and the Cyrillic letter И.
In Modern Greek the letter represents a Close front unrounded vowel . In Classical Greek, it was pronounced as a long Open-mid front unrounded vowel: . The symbol was initially used to denote the Voiceless glottal fricative (later spelled with a rough breathing). It was inherited as such by the Etruscan and Latin alphabets from the Cumaean alphabet in the 8th century BC, and this led to its subsequent universal usage in Western Europe as the letter H.
In the Ionic dialect however, this sound had disappeared by the sixth century BC, and the letter was re-used to represent the long . When the Ionic alphabet was adopted in Athens in 403 BC, (previously written as Ε) was also represented as Η there too, hence the modern Greek usage.

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Eta is sometimes used in place of eng (ŋ) when eng is not available, because of their similar appearance.
The upper-case letter Η is used as a symbol in:

★ Textual criticism, the Alexandrian text-type (from ''Hesychius'', its once-supposed editor).

★ Chemistry, enthalpy. H as symbol of enthalpy sometimes is said to a Greek eta, but enthalpy comes from ἐνθάλπος, beginning with epsilon, so more properly this H is a Latin aitch, from the word heat.
The lower-case letter η is used as a symbol in:

★ Thermodynamics, the efficiency of a Carnot heat engine.

★ Chemistry, the hapticity, or the number of electrons shared between a metal center and a ligand in a coordination compound. For example, an allyl group can coordinate to palladium in the η¹ mode or the η³ mode.

★ Optics, the refractive index of an optical medium (although the letter ''n'' is more common). It may also refer to the electromagnetic impedance of a medium.

★ Particle physics, to represent the η mesons.

★ Quantum Field Theory (physics), to represent the metric tensor.

★ Statistics, ''η''² is the "partial regression coefficient". ''η'' is the symbol for the linear predictor of a generalized linear model, and can also be used to denote the median of a population.

★ Economics, ''η'' is the elasticity.

★ Astronomy, the seventh brightest (usually) star in a constellation. ''See'' Bayer designation.

★ Experimental particle physics, η stands for pseudorapidity.

★ Mathematics, η-conversion, see lambda calculus

★ Fluid dynamics, η stands for viscosity.

★ Mathematics, the Dirichlet eta function, Dedekind eta function, and Weierstrass eta function.

★ Biology, a DNA polymerase found in higher eukaryotes and implicated in Translesion Synthesis.

★ Neural network backpropagation, η stands for the learning rate.