"Greek letters used in mathematics, science, and engineering Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities. Those Greek letters which have the same form as Latin letters are rarely used: capital A, B, E, Z, H, I, K, M, N, O, P, T, Y, X. Small ι, ο and υ are also rarely used, since they closely resemble the Latin letters i, o"
"E (mathematical constant) The number is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of as approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series The constant can be characterized in many different ways. For example, can be defined as the unique positive number such that the graph of the function has unit slope at . The function is called the (natural)"
"of his program Metafont approach . The versions are 2, 2.7, 2.71, 2.718, and so forth. E (mathematical constant) The number is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is approximately equal to 2.71828, and is the limit of as approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series The constant can be characterized in many different ways. For example, can be defined as the unique positive number such that"
"to 2.71828, and the Euler–Mascheroni constant γ (gamma) sometimes referred to as just ""Euler's constant"", approximately equal to 0.57721. It is not known whether γ is rational or irrational. Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function and was the first to write ""f""(""x"") to denote the function ""f"" applied to the argument ""x"". He also introduced the modern notation for the trigonometric functions, the letter for the base of the natural logarithm (now also known as Euler's number), the Greek letter Σ for summations"
"Pi The number () is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter """" since the mid-18th century, though it is also sometimes spelled out as ""pi"". It is also called Archimedes' constant. Being an irrational number, cannot be expressed as a common fraction (equivalently, its decimal representation never ends and never settles into a permanently repeating pattern). Still, fractions such"
"important constants, the symbols may be more complex and have an extra letter, an asterisk, a number, a lemniscate or use different alphabets such as Hebrew, Cyrillic or Gothic. Sometimes, the symbol representing a constant is a whole word. For example, American mathematician Edward Kasner's 9-year-old nephew coined the names googol and googolplex. The names are either related to the meaning of the constant (universal parabolic constant, twin prime constant, ...) or to a specific person (Sierpiński's constant, Josephson constant, ...). Abbreviations used: Mathematical constant A mathematical constant is a special number that is ""significantly interesting in some way"". Constants"
"Lévy's constant In mathematics Lévy's constant (sometimes known as the Khinchin–Lévy constant) occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions. In 1935, the Soviet mathematician Aleksandr Khinchin showed that the denominators ""q"" of the convergents of the continued fraction expansions of almost all real numbers satisfy for some constant γ. Soon afterward, in 1936, the French mathematician Paul Lévy found the explicit expression for the constant, namely The term ""Lévy's constant"" is sometimes used to refer to formula_3 (the logarithm of the above expression), which is approximately equal to 1.1865691104… The"
"1 2 3 4 E 2 - 1 2 3 4 5 6 E 2 + 1 2 3 E 1 × for a displayed result of 6.8880 -01 (representing , or 0.68880). Four constants are printed on the calculator case for easy reference. For converting to and from base 10 logarithms and natural logarithms the natural logarithm of 10 (2.30259) and e (2.71828) are printed on the case. Pi (3.14159) and 57.2958 (180 / Pi) are also on the case for trigonometry calculations. There was not enough internal memory to store these constants internally. Angles are computed using radians;"
"made the term Legendre's constant mostly only of historical value, with it often (technically incorrectly) being used to refer to Legendre's first guess 1.08366... instead. Pierre Dusart proved in 2010 Legendre's constant Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function formula_1. Its value is now known to be exactly 1. Examination of available numerical evidence for known primes led Legendre to suspect that formula_1 satisfies an approximate formula. Legendre conjectured in 1808 that where formula_4... Or similarly, where ""B"" is Legendre's constant. He guessed ""B"""
"Stieltjes constants In mathematics, the Stieltjes constants are the numbers formula_1 that occur in the Laurent series expansion of the Riemann zeta function: The constant formula_3 is known as the Euler–Mascheroni constant. The Stieltjes constants are given by the limit Cauchy's differentiation formula leads to the integral representation Various representations in terms of integrals and infinite series are given in works of Jensen, Franel, Hermite, Hardy, Ramanujan, Ainsworth, Howell, Coppo, Connon, Coffey, Choi, Blagouchine and some other authors. In particular, Jensen-Franel's integral formula, often erroneously attributed to Ainsworth and Howell, states that where δ is the Kronecker symbol (Kronecker delta)."
"three Unicode characters semantically represent mathematical constants: , the , and . Other mathematical constants can be represented using characters that have multiple semantic uses. For example, although Unicode includes a character for ""natural exponent"" ℯ (U+212F) its UCS canonical name derives from its glyph: ; and the mathematical constant π, 3.141592.., is represented by . The Western Arabic numerals also appear among the compatibility characters as rich text variant forms including bold, double-struck, monospace, sans-serif and sans-serif bold. and fullwidth variants for legacy vertical text support. Rich text parenthesized, circled and other variants are also included in the blocks:"
"using continued fractions to perform various studies, including statistical analysis. Many mathematical constants have an analytic form, that is they can be constructed using well-known operations that lend themselves readily to calculation. Not all constants have known analytic forms, though; Grossman's constant and Foias' constant are examples. Symbolizing constants with letters is a frequent means of making the notation more concise. A standard convention, instigated by Leonhard Euler in the 18th century, is to use lower case letters from the beginning of the Latin alphabet formula_15 or the Greek alphabet formula_16 when dealing with constants in general. However, for more"
"600 digits using Clenshaw–Curtis integration. Fransén–Robinson constant The Fransén–Robinson constant, sometimes denoted ""F"", is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive ""x"" axis. That is, The Fransén–Robinson constant has numerical value ""F"" = 2.8077702420285... , with the continued fraction representation [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] . Its proximity to Euler's number ""e"" = 2.71828... follows from the fact that the integral can be approximated by the standard series for ""e"". The difference is given by and also by"
"is The two digits in parentheses are the uncertainty (standard deviation) in the last two digits of the value. The relative uncertainty is . Some have suggested that it might be appropriate to name the symbol ""R"" the Regnault constant in honour of the French chemist Henri Victor Regnault, whose accurate experimental data were used to calculate the early value of the constant; however, the exact reason for the original representation of the constant by the letter ""R"" is elusive. The gas constant occurs in the ideal gas law, as follows: where ""P"" is the absolute pressure (SI unit pascals),"
", was in correspondence from Gottfried Leibniz to Christiaan Huygens in 1690 and 1691. Leonhard Euler introduced the letter as the base for natural logarithms, writing in a letter to Christian Goldbach on 25 November 1731. Euler started to use the letter for the constant in 1727 or 1728, in an unpublished paper on explosive forces in cannons, and the first appearance of in a publication was in Euler's ""Mechanica"" (1736). While in the subsequent years some researchers used the letter , the letter was more common and eventually became standard. The constant has been historically typeset as """", in"
"corresponding form of ""literal constant"". The numeric types codice_3 and codice_4 can only be signed (there is no concept of sign for type codice_5). Integer literal constants of the default kind take the form 1 0 -999 32767 +10 Kind can be defined as a named constant. If the desired range is ±10, the portable syntax for defining the appropriate kind, codice_11 is INTEGER, PARAMETER :: two_bytes = SELECTED_INT_KIND(4) that allows subsequent definition of constants of the form -1234_two_bytes +1_two_bytes Here, codice_11 is the kind type parameter; it can also be an explicit default integer literal constant, like -1234_2 but"
"Euler–Mascheroni constant The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural logarithm: Here, formula_2 represents the floor function. The numerical value of the Euler–Mascheroni constant, to 50 decimal places, is: The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled ""De Progressionibus harmonicis observationes"" (Eneström Index 43). Euler used the notations and for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations"
"will be irrational. E.g. primes of the form 4""n"" + 1 or 8""n"" + 1. By Dirichlet's theorem, the arithmetic progression ""dn""·10 + ""a"" contains primes for all ""m"", and those primes are also in ""cd"" + ""a"", so the concatenated primes contain arbitrarily long sequences of the digit zero. In base 10, the constant is a normal number, a fact proven by Arthur Herbert Copeland and Paul Erdős in 1946 (hence the name of the constant). The constant is given by where ""p"" is the ""n""th prime number. Its continued fraction is [0; 4, 4, 8, 16, 18, 5,"
"Glaisher–Kinkelin constant In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted ""A"", is a mathematical constant, related to the K-function and the Barnes G-function. The constant appears in a number of sums and integrals, especially those involving Gamma functions and zeta functions. It is named after mathematicians James Whitbread Lee Glaisher and Hermann Kinkelin. Its approximate value is: The Glaisher–Kinkelin constant formula_2 can be given by the limit: where formula_4 is the K-function. This formula displays a similarity between ""A"" and which is perhaps best illustrated by noting Stirling's formula: which shows that just as is obtained from approximation"
"Coulomb's constant Coulomb's constant, the electric force constant, or the electrostatic constant (denoted , or ) is a proportionality constant in electrodynamics equations. In SI units, it is exactly equal to , or roughly equaling . It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law. Coulomb's constant is the constant of proportionality in Coulomb's law, where is a unit vector in the -direction and where is the fine-structure constant, is the speed of light, is the reduced Planck constant, and is elementary charge. In SI: where formula_4 is the vacuum permittivity. This formula can"
"constant (or radiation density constant) ""a"" which is given by: Stefan–Boltzmann constant The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter ""σ"" (sigma), is the constant of proportionality in the Stefan–Boltzmann law: ""the total intensity radiated over all wavelengths increases as the temperature increases"", of a black body which is proportional to the fourth power of the thermodynamic temperature. The theory of thermal radiation lays down the theory of quantum mechanics, by using physics to relate to molecular, atomic and sub-atomic levels. Slovenian physicist Josef Stefan formulated the constant in 1879, and it was later"
"Gauss's constant In mathematics, Gauss's constant, denoted by ""G"", is defined as the reciprocal of the arithmetic–geometric mean of 1 and the square root of 2: The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered that so that where Β denotes the beta function. Gauss's constant should not be confused with the Gaussian gravitational constant. Gauss's constant may be used to express the gamma function at argument : Alternatively, and since and Γ() are algebraically independent, Gauss's constant is transcendental. Gauss's constant may be used in the definition of the lemniscate constants, the first of"
"an algebraic number of degree 71. This fact was proven by Conway, and the constant λ is known as Conway's constant. The same result also holds for every variant of the sequence starting with any seed other than 22. Conway's constant is the unique positive real root of the following polynomial: In his original article, Conway gives an incorrect value for this polynomial, writing − instead of + in front of formula_4. However, the value of given in his article is correct. The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the"
"constant grows linearly in ""n"". Alternatively, the Hermite constant ""γ"" can be defined as the square of the maximal systole of a flat ""n""-dimensional torus of unit volume. The Hermite constant is known in dimensions 1–8 and 24. For ""n"" = 2, one has ""γ"" = . This value is attained by the hexagonal lattice of the Eisenstein integers.. It is known that A stronger estimate due to Hans Frederick Blichfeldt is where formula_3 is the gamma function. Hermite constant In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space"
"Fransén–Robinson constant The Fransén–Robinson constant, sometimes denoted ""F"", is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive ""x"" axis. That is, The Fransén–Robinson constant has numerical value ""F"" = 2.8077702420285... , with the continued fraction representation [2; 1, 4, 4, 1, 18, 5, 1, 3, 4, 1, 5, 3, 6, ...] . Its proximity to Euler's number ""e"" = 2.71828... follows from the fact that the integral can be approximated by the standard series for ""e"". The difference is given by and also by The Fransén–Robinson constant can also"
"Faraday constant The Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is named after Michael Faraday. In physics and chemistry, this constant represents the magnitude of electric charge per mole of electrons. It has the currently accepted value This constant has a simple relation to two other physical constants: where ""N"" is the Avogadro constant (the ratio of the number of particles, ""N"", which is unitless, to the amount of substance, ""n"", in units of moles), and ""e"" is the elementary charge or the magnitude of the charge of an electron. This relation holds because the amount"
"Loschmidt constant The Loschmidt constant or Loschmidt's number (symbol: ""n"") is the number of particles (atoms or molecules) of an ideal gas in a given volume (the number density). It is usually quoted at standard temperature and pressure, the 2010 CODATA recommended value is per cubic metre at 0 °C and 1 atm and the 2006 CODATA recommended value was 2.686 7774(47) per cubic metre at 0 °C and 1 atm. It is named after the Austrian physicist Johann Josef Loschmidt, who was the first to estimate the physical size of molecules in 1865. The term ""Loschmidt constant"" is also"
"Conic constant In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter ""K"". For negative ""K"" it is given by where ""e"" is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is where ""K"" is the conic constant and ""R"" is the radius of curvature at ""x"" = 0. This formulation is used in geometric optics to specify oblate elliptical (""K"" > 0), spherical (""K"" = 0), prolate elliptical (0 > ""K"""
"Stefan–Boltzmann constant The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the Greek letter ""σ"" (sigma), is the constant of proportionality in the Stefan–Boltzmann law: ""the total intensity radiated over all wavelengths increases as the temperature increases"", of a black body which is proportional to the fourth power of the thermodynamic temperature. The theory of thermal radiation lays down the theory of quantum mechanics, by using physics to relate to molecular, atomic and sub-atomic levels. Slovenian physicist Josef Stefan formulated the constant in 1879, and it was later derived in 1884 by Austrian physicist Ludwig Boltzmann. The equation"
"Mills' constant In number theory, Mills' constant is defined as the smallest positive real number ""A"" such that the floor function of the double exponential function is a prime number, for all natural numbers ""n"". This constant is named after William H. Mills who proved in 1947 the existence of ""A"" based on results of Guido Hoheisel and Albert Ingham on the prime gaps. Its value is unknown, but if the Riemann hypothesis is true, it is approximately 1.3063778838630806904686144926... . The primes generated by Mills' constant are known as Mills primes; if the Riemann hypothesis is true, the sequence begins"
"Molar mass constant The molar mass constant, symbol ""M"", is a physical constant which relates relative atomic mass and molar mass. Its value is defined to be 1 g/mol in SI units. The molar mass constant is important in writing dimensionally correct equations. It is common to see phrases such as However, atomic weight, i.e., relative atomic mass, is a dimensionless quantity, and cannot take the units of grams per mole. Formally, the operation is the multiplication by a constant which has the value 1 g/mol, that is the molar mass constant. The molar mass constant is unusual (but not"
"constant). Alpha also stands for thermal expansion coefficient of a compound in physical chemistry. It is also commonly used in mathematics in algebraic solutions representing quantities such as angles. Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses. In zoology, it is used to name the dominant individual in a wolf or dog pack. The proportionality operator ""∝"" (in Unicode: U+221D) is sometimes mistaken for alpha. The uppercase letter alpha is not generally used as a symbol because it tends to"
"which is: and the second constant: which arise in finding the arc length of a lemniscate. A formula for ""G"" in terms of Jacobi theta functions is given by as well as the rapidly converging series The constant is also given by the infinite product It appears in the evaluation of the integrals Gauss' constant as a continued fraction is [0, 1, 5, 21, 3, 4, 14, ...]. Gauss's constant In mathematics, Gauss's constant, denoted by ""G"", is defined as the reciprocal of the arithmetic–geometric mean of 1 and the square root of 2: The constant is named after Carl"