英语词汇“gamma function”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

gamma function n. a function (symbol Γ) which extends the notion of factorial n (written n!) from positive whole numbers to real and complex variables, given by Γ(z) = ∫∞0t^{z − 1}e^−tdt.The function has the properties that Γ(z) = (z − 1)!, and Γ(z + 1) = zΓ(z), and is undefined for values of z that are negative whole numbers or zero. The incomplete gamma function is obtained by varying one or other of the limits of integration in the defining equation.The function was devised by Euler in 1729 ( L. Euler Let. 13 Oct. 1729 , in P. H. Fuss Correspondance mathématique et physique (1843) I. 3–4), but not named by him; the name and symbol Γ were given by Legendre in 1809 ( Mém. de la classe des sci. mathématiques et physiques de l'Inst. de France, année 1809 (1810) 477; also A. M. Legendre Exercises de calcul intégral (1811) I. ii. 277).

ΘΚΠ

the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral

fluent1706

integral1728

gamma function1834

surface integral1867

Riemann integral1894

Cauchy's integral1898

Lebesgue integral1905

Stieltjes integral1914

convolution1934

1834 Rep. Brit. Assoc. Advancem. Sci. 1833 222 (note) Legendre has named the function Γ (1 + r) = 1. 2... r, the function gamma.

1843 Penny Cycl. XXV. 120/2 One of the first of these [transcendental quantities] will be the well-known function of n, which is generally designated by Γn, and is sometimes called the gamma-function, sometimes the factorial function.

1875 B. Williamson Elem. Treat. Integral Calculus (rev. ed.) 150 All definite integrals which are reducible to Gamma-functions.

1908 T. J. I'A. Bromwich Introd. Theory Infinite Series 461 (heading) Stirling's asymptotic formula for the gamma-function when x is real, large and positive.

1922 Jrnl. Inst. Actuaries 53 309 The incomplete Γ-function..is not convenient, as it stands, either for tabulation or for computation.

1998 A. A. Vigasin in A. A. Vigasin & Z. Slanina Molecular Complexes in Earth's Planetary, Cometary & Interstellar Atmospheres i. 18 Integration over E yields an incomplete gamma-function.

2005 Brit. Jrnl. Hist. Sci. 38 200 He devoted much of his energy to exploring gamma functions, integral equations and the behaviour of asymptotic expansions.

单词	gamma function
释义	> as lemmas gamma function gamma function n. a function (symbol Γ) which extends the notion of factorial n (written n!) from positive whole numbers to real and complex variables, given by Γ(z) = ∫∞0t^{z − 1}e^−tdt.The function has the properties that Γ(z) = (z − 1)!, and Γ(z + 1) = zΓ(z), and is undefined for values of z that are negative whole numbers or zero. The incomplete gamma function is obtained by varying one or other of the limits of integration in the defining equation.The function was devised by Euler in 1729 ( L. Euler Let. 13 Oct. 1729 , in P. H. Fuss Correspondance mathématique et physique (1843) I. 3–4), but not named by him; the name and symbol Γ were given by Legendre in 1809 ( Mém. de la classe des sci. mathématiques et physiques de l'Inst. de France, année 1809 (1810) 477; also A. M. Legendre Exercises de calcul intégral (1811) I. ii. 277). ΘΚΠ the world > relative properties > number > calculus > [noun] > integral calculus > integration or integrability > integral fluent1706 integral1728 gamma function1834 surface integral1867 Riemann integral1894 Cauchy's integral1898 Lebesgue integral1905 Stieltjes integral1914 convolution1934 1834 Rep. Brit. Assoc. Advancem. Sci. 1833 222 (note) Legendre has named the function Γ (1 + r) = 1. 2... r, the function gamma. 1843 Penny Cycl. XXV. 120/2 One of the first of these [transcendental quantities] will be the well-known function of n, which is generally designated by Γn, and is sometimes called the gamma-function, sometimes the factorial function. 1875 B. Williamson Elem. Treat. Integral Calculus (rev. ed.) 150 All definite integrals which are reducible to Gamma-functions. 1908 T. J. I'A. Bromwich Introd. Theory Infinite Series 461 (heading) Stirling's asymptotic formula for the gamma-function when x is real, large and positive. 1922 Jrnl. Inst. Actuaries 53 309 The incomplete Γ-function..is not convenient, as it stands, either for tabulation or for computation. 1998 A. A. Vigasin in A. A. Vigasin & Z. Slanina Molecular Complexes in Earth's Planetary, Cometary & Interstellar Atmospheres i. 18 Integration over E yields an incomplete gamma-function. 2005 Brit. Jrnl. Hist. Sci. 38 200 He devoted much of his energy to exploring gamma functions, integral equations and the behaviour of asymptotic expansions. extracted from gamman.adj. < as lemmas
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> as lemmas