Digamma - Wikipedia
WebDigamma or wau (uppercase: Ϝ, lowercase: ϝ, numeral: ϛ) is an archaic letter of the Greek alphabet. It originally stood for the sound / w / but it has remained in use principally as a Greek numeral for 6 .
Digamma function - Wikipedia
WebReal part plots of the digamma and the next three polygamma functions along the real line. In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: [1] [2] [3] It is the first of the polygamma functions.
Digamma - Simple English Wikipedia, the free encyclopedia
WebDigamma or Wau (uppercase/lowercase Ϝ ϝ ς) was an old letter of the Greek alphabet. It was used before the alphabet converted its classical standard form. It looked like a Latin "F", but it was pronounced like "w". In the 5th century BC, people stopped using it because they could no longer pronounce the sound "w" in Greek.
Trigamma function - Wikipedia
WebIn mathematics, the trigamma function, denoted ψ1(z) or ψ(1)(z), is the second of the polygamma functions, and is defined by. . It follows from this definition that. where ψ(z) is the digamma function. It may also be defined as the sum of the series.
Digamma | ancient Greek letter | Britannica
WebChalcidian alphabet, one of several variants of the Greek alphabet, used in western Greece (Évvoia) and in some of the Greek colonies in Italy (Magna Graecia); probably ancestral to the Etruscan alphabet. See Greek alphabet.
Digamma Function | Brilliant Math & Science Wiki
WebThe digamma function usually denoted by \ (\psi\) is defined as the logarithmic derivative of the gamma function . Definition. Functional Equation. Series Representation. Integral Representation. Euler's Reflection Formula. Legendre Duplication Formula. Applications in Summations. Polygamma Functions. Example Problems. Implementation in Mathematica
Digamma function: Introduction to the differentiated gamma …
WebDefinitions of the differentiated gamma functions. The digamma function , polygamma function , harmonic number , and generalized harmonic number are defined by the following formulas (the first formula is a general definition for complex arguments and the second formula is for positive integer arguments): Here is the Euler gamma constant:
Digamma Function -- from Wolfram MathWorld
WebThe digamma function is a special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial ). Because of this ambiguity, two different notations are sometimes (but not always) used, with. (1)
complex analysis - Asymptotic Expansion of Digamma Function ...
WebFeb 12, 2021 · While reading the wikipedia page of the Digamma function ( https://en.wikipedia.org/wiki/Digamma_function#Asymptotic_expansion) I noticed that it said the asymptotic expansion for the digamma function ( ψ(z) ψ ( z)) can be obtained from using. ψ(z + 1) = −γ +∑n=1∞ ( 1 n − 1 n + z) ψ ( z + 1) = − γ + ∑ n = 1 ∞ ( 1 n − 1 n …
Polygamma function - Wikipedia
Webholds where ψ(z) is the digamma function and Γ (z) is the gamma function. They are holomorphic on . At all the nonpositive integers these polygamma functions have a pole of order m + 1. The function ψ(1)(z) is sometimes called the trigamma function . Integral representation. When m > 0 and Re z > 0, the polygamma function equals.
Digamma function: Introduction to the differentiated gamma …
WebIn his famous work, J. Stirling (1730) not only found the asymptotic formula for factorial , but used the digamma psi function (related to the harmonic numbers), which is equal to the derivative of the logarithm from the gamma function (). Later L. Euler (1740) also used harmonic numbers and introduced the generalized harmonic numbers .
Properties of Digamma Function - ProofWiki
WebMar 16, 2024 · Theorem. This page gathers together some of the properties of the digamma function : The digamma function, ψ ψ, is defined, for z ∈C ∖Z≤0 z ∈ C ∖ Z ≤ 0, by the logarithmic derivative of the gamma function : ψ(z) = Γ′(z) Γ(z) ψ ( z) = Γ ′ ( z) Γ ( z) where Γ Γ is the gamma function, and Γ′ Γ ′ denotes its derivative .
digamma - Wiktionary, the free dictionary
WebApr 8, 2024 · digamma m ( invariable) Italian Wikipedia has an article on: digamma. digamma (Old Greek letter Ϝ, ϝ) ( archaic, phonetics) the semivowel /u̯/. a letter with a shape similar to that of digamma : the Claudian letter Ⅎ. the Old Italic letter 𐌅. ( obsolete) the Latin letter F.
complex analysis - Digamma function - Mathematics Stack …
WebJan 9, 2020 · The Wikipedia lists several integral representations for digamma: en.wikipedia.org/wiki/Digamma_function#Integral_representations . MathWorld gives at least one more. mathworld.wolfram.com/DigammaFunction.html And the DLMF has a few as well. dlmf.nist.gov/5.9.
Digamma — Wikipédia
WebDigamma [(capitale : Ϝ, minuscule : ϝ) en grec δίγαμμα [1], c'est-à-dire gamma double] est une lettre archaïque de l'alphabet grec. Dérivée de la lettre wāu de l'alphabet phénicien, elle a été utilisée pour transcrire la consonne spirante labio-vélaire voisée / w / héritée de l’indo-européen commun.
Digamma - Wikipedia
WebThe name digamma was used in ancient Greek and is the most common name for the letter in its alphabetic function today. It literally means "double gamma " and is descriptive of the original letter's shape.
Greek letters used in mathematics, science, and engineering
WebThe archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used. The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet before switching to Latin letters.
Digamma Radiation - HBM's Nuclear Tech Wiki
WebApr 21, 2024 · Digamma radiation (symbol: ; shortened: DRX, counted in mDRX and mDRX/s) is a (fictional) incremental effect that only targets entities, not inanimate objects, unlike regular radiation. It is not a spectrum of waves or charged particles per se, so even the densest of materials will not shield you from it.
Digamma – Wikipedia
WebDigamma, alun perin wau (isona kirjaimena Ϝ, pienenä ϝ, m.kreik. Ϝαῦ, kreik. δίγαμμα), on käytöstä pois jäänyt kirjain kreikkalaisessa kirjaimistossa. Sen äännearvo muinaiskreikassa oli [w]. Digammaa käytettiin vielä arkaaisella kaudella. Se oli aakkosissa kuudentena, epsilonin ja zeetan välissä.
Digamma – Wikipédia
WebA digamma (Ͷͷ, régies forma: Ϝϝ) a preklasszikus görög ábécé hatodik betűje. Archaikus neve, melyet ma már ritkán használnak, vau . Ez a betű korán kikerült az ábécéből, még az úgynevezett „klasszikus” kor előtt. Csak a kisbetűs formáját használták, nagybetűs alakját csak később, a középkor során alakították ki. Hangértéke valószínűleg /w/ volt.
Stigma (ligature) - Wikipedia
WebOriginally called wau, it was called digamma in classical Greek and episemon during the Byzantine era. It was conflated with the στ ligature owing to the accidental similarities of their shapes.
Digamma – Wikipedia
WebDigamma ( grekiska δίγαμμα dígamma, av δί- dí- ’två’ och γάμμα gámma ’ gamma ’) ( versal: Ϝ, gemen: ϝ) var ursprungligen den sjätte bokstaven i det grekiska alfabetet och hade därför i det joniska talbeteckningssystemet siffervärdet 6. I modern grekiska används stigma (ς) i denna funktion.
Claudian letters - Wikipedia
WebClaudian letters with the Ↄ variant of antisigma. Claudian pomerium marker, where written words ampliavit and terminavit use turned digamma (highlighted in red) The Claudian letters were developed by the Roman emperor Claudius (reigned 41–54). He introduced three new letters to the Latin alphabet :
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