Rho

Rho 'roʊ (uppercase Ρ, lowercase ρ or ; ρο or ρω) is the seventeenth letter of the Greek alphabet. In the system of Greek numerals it has a value of 100. It is derived from Phoenician letter res . Its uppercase form uses the same glyph, Ρ, as the distinct Latin letter P; the two letters have different Unicode encodings. Rho is classed as a liquid consonant (together with Lambda and sometimes the nasals Mu and Nu), which has important implications for morphology. In both Ancient and Modern Greek, it represents a alveolar trill r, alveolar tap ɾ, or alveolar approximant ɹ. In polytonic orthography, a rho at the beginning of a word is written with a rough breathing, equivalent to h (ῥ rh), and a double rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second (ῤῥ rrh). That apparently reflected an aspirated or voiceless pronunciation in Ancient Greek, which led to the various Greek-derived English words starting with rh or containing rrh. The name of the letter is written in Greek as ῥῶ (polytonic) or ρω/ρο (monotonic). Letters that arose from rho include Roman R and Cyrillic Er (Р). The characters ρ and are also conventionally used outside the Greek alphabetical context in science and mathematics. In the physical sciences to represent: Densities: mass density, air density or charge density (ρ) Resistivity (ρ) Rho meson (ρ+, ρ−, ρ0) General quantum states Hammett Equation, ρ is used to represent the reaction constant, this is independent of the position and nature of the substituents of the benzene ring. In mathematics to represent: A length coordinate in polar, cylindrical, spherical, and toroidal coordinate systems, and toroidal and poloidal coordinates of the Earth's magnetic field. The correlation coefficient of a population parameter The spectral radius of a matrix denoted as The plastic number The prime constant The sensitivity to interest rates of a pricing function The expected return of a given policy () in reinforcement learning, denoted In economics to represent the discount rate of future pence cash flows In molecular biology to represent the Rho protein responsible for termination of RNA synthesis.