Gamma functions with charactersHurwitz's L-functionsShintani functionsThe main objective of this paper is to define Gamma-functions Gamma[chi](v) with characters chi and study their properties. To this end, we ought to introduce L-functions L(s; chi, v) = Sigma(infinity)(n=0) chi(n+1)...
gamma(<rate>) <rate>. Numeric value specifying the shape parameter for the distribution. This values must be greater than 0. Description Specifies a gamma distribution for the probability scale. Examples Figure 1. Example: Specifying a gamma distribution for the probability scale SCALE: prob(dim...
rev=1.6&content-type=text/plain&cvsroot=src##/* Method:## * 1. Argument Reduction for 0 < x <= 8## * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may## * reduce x to a number in [1.5,2.5] by## * lgamma(1+s) = log(s) + lgamma(s)## * for example,## ...
大数入门 (4) Omega Level Functions(搬运/生肉) 10伊翔 39 0 大数入门 (12) Theta in the Fast Growing Hierarchy(搬运/生肉) 10伊翔 21 0 大数入门 (3) Fast Growing Hierarchy(搬运/生肉) 10伊翔 43 0 大数入门 (2) Graham's Number(搬运/生肉) 10伊翔 19 0 大数入门 (5) Epsilon Level...
gamma functiondigamma and polygamma functionsrate of convergencecompletely monotonic functioninequalitiesEuler-Mascheroni constantWe propose a new sharp family of approximations which improve the results of Sandor and Debnath [On certain inequalities involving the constant e and their applications, J. Math. ...
Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions Abstract As we have shown in Section 2.2.8, irreducible finite dimensional representations of commutative groups are one-dimensional. In particular, ...
GENERALIZED GAMMA FUNCTIONS WITH CHARACTERS.GENERALIZED GAMMA FUNCTIONS WITH CHARACTERS.GammafunctionswithcharactersHurwitz'sShintanifunctionsThe main objective of this paper is to define Γ-functions Γ[χ](v) with characters χ and study their properties. To this end, we ought to introduce L-functions...
both Format #include <math.h> double gamma(doublex); Compiler option:LANGLVL(SAA), LANGLVL(SAAL2), orLANGLVL(EXTENDED) General description gamma() provides the same function as lgamma(), including the use ofsigngam. Use of lgamma() instead of gamma() is suggested byXPG4.2. ...
Let $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$ , $\psi '(x)$ , and $\psi ''(x)$ are, respectively, called the digamma, trigamma, and tetragam