Greek alphabetThe Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic and early Classical times, the Greek alphabet existed in many local variants, but, by the end of the 4th century BC, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today.
Greek diacriticsGreek orthography has used a variety of diacritics starting in the Hellenistic period. The more complex polytonic orthography (πολυτονικό σύστημα γραφής), which includes five diacritics, notates Ancient Greek phonology. The simpler monotonic orthography (μονοτονικό σύστημα γραφής), introduced in 1982, corresponds to Modern Greek phonology, and requires only two diacritics. Polytonic orthography () is the standard system for Ancient Greek and Medieval Greek.
Digraph (orthography)A digraph or digram (from the δίς , "double" and γράφω , "to write") is a pair of characters used in the orthography of a language to write either a single phoneme (distinct sound), or a sequence of phonemes that does not correspond to the normal values of the two characters combined. Some digraphs represent phonemes that cannot be represented with a single character in the writing system of a language, like the English sh in ship and fish. Other digraphs represent phonemes that can also be represented by single characters.
Hermite polynomialsIn mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term is present); systems theory in connection with nonlinear operations on Gaussian noise.
Legendre polynomialsIn mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.
