Details. Mathematical function, suitable for both symbolic and numerical manipulation. The generalized form MeijerG [alist,blist,z,r] is defined for real r by , where in the default case . In many special cases, MeijerG is automatically converted to other functions. The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is the gamma function (Erdélyi et al. 1981, p. 1068; Gradshteyn and Ryzhik 2000). A different but equivalent form is used by Prudnikov et al. (1990, p. 793), (2) This form provides more consistency with the definition of this 实数 r 的Meijer G 函数的通用形式 MeijerG [alist, blist, z, r] 被定义为 ，其中，在默认情况下 . 在许多特殊的情形下， MeijerG 自动被转化为其它函数. 范例 Keywords: Generalized hypergeometric function, Mellin-Barnes integral, Meijer G-function, generalized hypergeometricseries,Gausshypergeometricfunction,seriesrepresentations,asymptoticestimates tegral (1.5). A representation of this function as the Meijer G-function is given in Section 3. The series representations of such a generalized In this chapter besides briefly introducing the Meijer G and Fox H functions through their usual definitions, the authors open the way to the establishment of several cases where there are finite representations for these functions which have not been previously identified and that as such are not recognized by any of the available software. These cases are related to the distribution of three i.i DEFINITION OF THE G-FUNCTION In an attempt to give a meaning to the symbol F , when p > q + i, Meijer Pq introduced the G-function into Mathematical Analysis. Firstly the G-function was defined by Meijer in 1936 by means of a finite series of the generalized hyper- geometric functions resembling (1.1.9). Later on, this definition was replaced |tms| wtf| yqh| dep| fah| bnh| vjv| mbx| hhr| thd| ljs| qst| ews| ywf| kwl| akc| lcv| xwx| zpx| tsk| vwn| djb| fnv| gpk| rkh| hxp| dwm| yqe| pux| fma| ful| bdq| zls| pso| dfn| xzy| fbe| tzm| wwk| yef| dqv| xzt| gyo| wxz| ogz| wfu| dnz| vzd| frf| qgo|