Nettetwith radial positive definite functions and generalizations of Luke’s inequalities for the Kummer and Gauss type functions. Keywords: generalized hypergeometric function, Meijer’s Gfunction, integral representation, radial positive definite function, inverse factorial series, Hadamard finite part MSC2010: 33C20, 33C60, 33F05, 42A82, 65D20 NettetIn this paper, we introduce and study a new class of harmonic convex functions which is called harmonic beta-preinvex functions. We establish some estimates, involving the Euler Beta function and the Hypergeometric function of the integral $\int_a^{a+\eta(b,a)}(x-a)^p(a+\eta(b,a)-x)^qf(x)\mathrm{d}x$ for the class of functions …
Hypergeometric function - Wikipedia
NettetBasic hypergeometric series. In mathematics, basic hypergeometric series, or q-hypergeometric series, are q -analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series xn is called hypergeometric if the ratio of successive terms xn+1 / xn is a rational function of n. Nettet19. okt. 2024 · The integration of the quotient of hypergeometric functions can be calculated or verified with the help of a CAS such as Mathematica. The Gaussian … dark blue and light blue walls
Numerical integration of a hypergeometric function
Nettet13. apr. 2024 · The classical hypergeometric summation theorems have a significant role in the theory of generalized hypergeometric functions. Over the years generalization … Nettet(Gauss 1812, Barnes 1908). To confuse matters even more, the term ”hypergeometric function” is less commonly used to mean closed form, and ”hypergeometric series” is … NettetA definite integral of a function can be represented as the signed area of the region bounded by its graph and the horizontal axis. ... In particular, it may be useful to have, … dark blue and mustard living room