asymptotics and closed form of a generalized incomplete gamma function abstract we consider the asymptotic behavior of the function x b x t 1 e t b t dt x 0 0 b 0 as x tends to infinity we give several expansions for the case that and b are fixed and we give a uniform expansion in which and b may range through unbounded intervals we give a closed form for half integer values of

unified probability density function involving a confluent hypergeometric function of two variables in this paper first we define a new gamma type function by means of an integral involving the confluent hypergeometric function of two variables f 1 a b c w z the gamma type function is expressed in explicit form using generalized hypergeometric series associated incomplete functions are defined some special cases are noted and some relations for the new gamma type function are given a generalized probability density is considered using the gamma type function this density represents a unified form for several gamma type and inverse gaussian densities a new probability density function with gauss hypergeometric function is obtained a number of known probability density functions follow as special cases some statistical functions associated with the new density are obtained some figures are drawn for the probability density to show the effect of the parameters involved results given recently by al zamel ali et al and others can be recovered from the formulas established here

on certain generalized incomplete gamma functions abstract recently chaudhry and zubair have introduced a generalized incomplete gamma function v x z which reduces to the incomplete gamma function v x when its variable z vanishes we show that v x z may be written essentially as a single kampe de feriet function which in turn may be expressed as a linear combination of two incomplete weber integrals then by using properties of the latter integrals we deduce additional representations for v x z in particular we show that v x z is essentially completely determined by a finite number of modified bessel functions for all v 0 provided we know the values of the two incomplete weber integrals when 0

extension of euler s beta function an extension of euler s beta function analogous to the recent generalization of euler s gamma function and riemann s zeta function for which the usual properties and representation are naturally and simply extended is introduced it is proved that the extension is connected to the macdonald error and whittaker functions in addition the extended beta distribution is introduced

extended hypergeometric and confluent hypergeometric functions an extension of the beta function by introducing an extra parameter which proved to be useful earlier is applied here to extend the hypergeometric and confluent hypergeometric functions since the latter functions contain many of the familiar special functions as sub cases this extension is expected to prove to be useful the object of the present paper is to study this extension and its relationship with the hypergeometric and confluent hypergeometric functions

homotopical variations and high dimensional zariski van kampen theorems we give a new definition of the homotopical variation operators occurring in a recent high dimensional zariski van kampen theorem a definition which opens the way to further generalizations of theorems of this kind

reduction formulae for kampe de feriet functions fq 1 0p 2 1 abstract several reduction formulae for kampe de feriet functions f q 1 0 p 2 1 are given in terms of a finite number of generalized hypergeometric functions

evaluations of certain euler type integrals abstract in this paper we obtain the evaluations of certain euler type integrals further we establish a theorem on extended beta function and apply this to obtain evaluations of some integrals in terms of extended beta function b a furthermore we derive a number of new results as applications of these evaluations we extend also some results of this paper to the multi variable case

deformations of the hemisphere that increase scalar curvature consider a compact riemannian manifold m of dimension n whose boundary m is totally geodesic and is isometric to the standard sphere s n 1 a natural conjecture of min oo asserts that if the scalar curvature of m is at least n n 1 then m is isometric to the hemisphere s n equipped with its standard metric this conjecture is inspired by the positive mass theorem in general relativity and has been verified in many special cases in this paper we construct counterexamples to min oo s conjecture in dimension n 3

normal forms for perturbed keplerian systems abstract perturbations of rotating and nonrotating keplerian systems with two and three degrees of freedom are considered the dominant unperturbed part of the hamilton function is the sum of the two body part and the coriolis term the flows associated to these two components are used to put the whole system into normal form by means of symplectic transformations three different situations are analysed i the two body effect dominates the coriolis part slow rotations ii the coriolis effect is stronger than the two body hamiltonian very fast rotations and iii the two effects are comparable moderate rotations after performing the transformations to normal form the system is reduced by one or two degrees of freedom we describe the reduced phase spaces by calculating the invariants of the symmetry groups associated to the different normal forms reduced systems the technique is applied to the reduction of a hamiltonian system modelling the trapping mechanisms for the electron of a strongly ionized hydrogen atom

incomplete lipschitz hankel integrals of macdonald functions abstract various representations for incomplete lipschitz hankel integrals of macdonald functions have been given in closed form using kampe de feriet double hypergeometric functions in addition reduction formulas for the kampe de feriet functions associated with these integrals have been derived in some cases

boundary effect of ricci curvature on a compact riemannian manifold with boundary we study how ricci curvature of the interior affects the geometry of the boundary first we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature then we discuss related rigidity questions and prove ricci curvature rigidity results for manifolds with boundary

generalized incomplete gamma functions with applications abstract in this paper we introduce new functions as generalizations of the incomplete gamma functions the functions are found to be useful in heat conduction probability theory and in the study of fourier and laplace transforms some important properties of the functions are studied we have investigated the asymptotic behavior laplace transforms special cases decomposition formula integral representations convolutions recurrence relations and differentiation formula of these functions applications of these functions in evaluation of certain inverse laplace transforms to the definite integrals and to the infinite series of exponential functions are shown

a certain generalized pochhammer symbol and its applications to hypergeometric functions in this article we first introduce an interesting new generalization of the familiar pochhammer symbol by means of a certain one parameter family of generalized gamma functions with the help of this new generalized pochhammer symbol we then introduce an extension of the generalized hypergeometric function rf s with r numerator and s denominator parameters finally we present a systematic study of the various fundamental properties of the class of the generalized hypergeometric functions introduced here

an incomplete lipschitz hankel integral of k0 on etudie k e0 a z 0 z exp at k 0 t dt ou k est la fonction de macdonald ou fonction de bessel d argument imaginaire on montre que k e0 a z peut s ecrire sous forme close en termes de fonctions elementaires k 0 k 1 et des fonctions hypergeometriques doubles de kampe de feriet

the asymptotic expansion of a generalised incomplete gamma function we define a generalised incomplete gamma function lp a z which coincides with the familiar normalised function q a z a z a when the integer parameter p 1 it is shown that the large z asymptotics of lp a z in the sector argz 0 all these expansions are recessive at infinity and form a sequence of increasingly subdominant exponential contributions

on the decomposition of generalized incomplete gamma functions with applications to fourier transforms abstract in this paper we introduce decomposition functions c x s x c x and s x of the generalized gamma functions these functions are found useful in the analytic study of the temperature distribution of a semi infinite solid with periodic boundary conditions and to the theory of fourier transforms several new identities involving the fourier transforms are investigated and some of the classical ones are recovered as special cases for numerical and scientific computations tabular and graphical representations of the functions c x and s x are also given

further reducible cases of certain kampe de fe riet functions associated with incomplete integrals of cylindrical functions abstract new reduction formulas are derived for the kampe de feriet functions f q 1 0 p 2 1 and f 1 2 1 1 1 0 which are closely connected with representations for incomplete lipschitz hankel type integrals of cylindrical functions some general series identities and related reduction formulas relevant to the present investigation are also considered

a note on hang wang s hemisphere rigidity theorem let m g be a compact manifold with boundary and ric g ge n 1 g hang and wang proved that m g is isometric to the standard hemisphere if partial m is convex and isometric to mathbb s n 1 1 we prove some rigidity theorems when partial m is isometric to a product manifold where one factor is the standard sphere

extended incomplete gamma functions with applications an extension of the generalized inverse gaussian density function is proposed analogous to a recent useful generalization of the incomplete gamma functions extensions of the generalized incomplete gamma functions are presented for which the usual properties and representations are naturally and simply extended several classical functions including abramowitz s functions dowson s integral function goodwin and stalon s function and astrophysical thermonuclear functions are proved to be special cases of these extensions in addition extended meijer g functions and fox s h functions are defined

incomplete bessel generalized incomplete gamma or leaky aquifer functions functions characterized by the alternative appelations in the title hereof have application in areas as diverse as heat conduction probability theory electronic structure in periodic systems and hydrology these functions are regarded as difficult to evaluate and have been given attention by a number of investigators in all these fields this communication ties together the previously disjoint literature and presents several new expansions of these functions that are in various parameter ranges computationally more efficient than any of the previously proposed methods of evaluation a new formula for computation of these functions from nearby tabulated values is also reported the computational advantages of the new procedures are illustrated with examples

extension of gamma beta and hypergeometric functions the main object of this paper is to present generalizations of gamma beta and hypergeometric functions some recurrence relations transformation formulas operation formulas and integral representations are obtained for these new generalizations

the estimation of laplace random vectors in additive white gaussian noise this paper develops and compares the maximum a posteriori map and minimum mean square error mmse estimators for spherically contoured multivariate laplace random vectors in additive white gaussian noise the mmse estimator is expressed in closed form using the generalized incomplete gamma function we also find a computationally efficient yet accurate approximation for the mmse estimator in addition this paper develops an expression for the mse for any estimator of spherically contoured multivariate laplace random vectors in additive white gaussian noise awgn the development of which again depends on the generalized incomplete gamma function the estimators are motivated and tested on the problem of wavelet based image denoising

on the approximation of a generalized incomplete gamma function arising in heat conduction problems abstract several asymptotic expansions are given for the generalized incomplete gamma function x b x t 1 e t b t dt x 0 re b 0 b 0 as x tends to infinity where the real parameter is allowed to take negative values in the case b i 0 we obtain the expansions of the decomposition functions c x and s x closed form expressions are also given for 3 2 5 2

analytic expressions and bounds for special functions and applications in communication theory this paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory these functions are the well known nuttall q function incomplete toronto function rice ie function and incomplete lipschitz hankel integrals capitalizing on the offered results useful identities are additionally derived between the above functions and humbert phi 1 function as well as for specific cases of the kampede feriet function these functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems such as cognitive radio cooperative and free space optical communications as well as radar diversity and multiantenna systems as an example new closed form expressions are derived for the outage probability over nonlinear generalized fading channels namely alpha eta mu alpha lambda mu and alpha kappa mu as well as for specific cases of the eta mu and lambda mu fading channels furthermore simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal to noise ratio for single antenna and multiantenna communication systems over rician fading channels the accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results

a sonine gegenbauer integral of the neumann function abstract motivated by a desire to express in closed form a certain potential occurring in the study of diffraction of a plane electromagnetic wave by a wedge miller and exton developed computable expressions for a large class of sonine gegenbauer type integrals in the present paper one of these integrals given previously in terms of generalized hypergeometric functions in three variables is now obtained in terms of hypergeometric functions in two variables thereby much reducing the complexity of the representation in the course of this investigation certain identities involving srivastava s f 3 function kampe de feriet functions and wright functions are deduced in addition evaluations of integrals of bessel functions related to the above analysis are provided

incomplete lipschitz hankel integrals of bessel functions abstract various representations for incomplete lipschitz hankel integrals of bessel functions have been given in terms of kampe de feriet double hypergeometric functions reduction formulas for the double series employed have been given in some cases keywords integrals of bessel functions hypergeometric functions

the generalization of special functions the question of what special functions should be taken to be is addressed using examples of generalizations that have proved useful with special reference to those developed by chaudhry and me an attempt is made to formulate criteria for guiding us in the search for worth while generalizations of special functions

sonine gegenbauer type integrals abstract representations for complete and incomplete sonine gegenbauer type integrals are given in terms of generalized hypergeometric functions in two and three variables and in terms of neumann type series certain interesting reductions of these integrals are also given in addition an application to a problem in diffraction theory is provided