Kummers confluent hypergeometric for complex arguments in. Confluent hypergeometric function of the first kind calculator high accuracy calculation welcome, guest. The confluent and gauss hypergeometric functions are examples of special func tions, whose theory and computation are prominent in the scientific literature 3, 6, 40, 53, 57, 58, 62, 73, 95, 97, 108. It is commonly denoted, or, and is also known as kummers function of the first kind. Many special functions are also expressible as special cases of 1f1, including the incomplete gamma function, bessel functions and laguerre. Thompson 1997, atlas for computing mathematical functions. An expansion of the confluent hypergeometric function ia, c, z in series of functions of the same kind has been given by buchholz 1. Numerical methods for the computation of the confluent and. A new fortran 90 program to compute regular and irregular. Series representations 19 formulas hypergeometric1f1.
A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. Enter your mobile number or email address below and well send you a link to download the free kindle app. Since the matrix variate confluent hypergeometric function kind 1 distribution is a generalization of the matrix variate gamma distribution, it is reasonable to say that the matrix variate confluent hypergeometric function kind 1 distribution can be used as an alternative to. The motivation for computing hypergeometric functions will be discussed, with details given of some of the practical applications of these functions. To download laheys cheap fortran 90 compiler click on elf90. Temme abstract for the confluent hypergeometric functions u a, b, z and m a, b, z asymptotic expansions are given for a,o. Confluent hypergeometric function of the first kind. Unfortunatey, the library can compute confluent hypergeometric function only for real values of a and b. For small, the function behaves as see also bateman function, confluent hypergeometric function of the first kind, confluent hypergeometric limit function, coulomb wave function, cunningham function, gordon function, hypergeometric function, poissoncharlier polynomial, toronto function. Special functions in fortran 90 choose a source program.
Heatley, transactions of royal society of canada, 1943, defines a function which is a confluent hypergeometric function in z2 multiplied by a power of z, and gives a short 5figure table. This has a wide variety of applications, including cir processes and pricing asian options. Then you can start reading kindle books on your smartphone, tablet, or computer no. Integral involving a confluent hypergeometric function. So this file may be considered as its generalization for complex a and b. This chapter is based in part on abramowitz and stegun 1964, chapter by l. The hypergeometric function the confluent hypergeometric functions. Fortran subroutines for the evaluation of the confluent hypergeometric functions by william b. These functions generalize the classical hypergeometric functions of gauss, horn, appell, and lauricella. I have not tried it myself, so comments would be welcome. An alternate form of the solution to the confluent hypergeometric differential equation is known as the whittaker function. There is an interpreter for a subset of fortran 90 available from. The whittaker functions give an alternative form of the solution.
Some applications on generalized hypergeometric and. Olde daalhuis school of mathematics, edinburgh university, edinburgh, united kingdom acknowledgements. How to express a hypergeometric confluent function in the pfq form. Hypergeometricpfqa 1,a 2,a 3,b 1,b 2,z 40964 formulas primary definition 2 formulas specific values 40747 formulas general characteristics 23 formulas series representations 40 formulas integral representations 5 formulas. Kummers function satisfies a secondorder linear differential equation called the confluent hypergeometric equation. Fortran subroutines for the evaluation of the confluent hypergeometric functions by gragg, william bneta, beny. Calculates confluent hypergeometric function of the first kind or kummers function ma,b,z. The integral representation of the confluent hypergeometric m function is note that the standard form is ma,b,z.
Expansion of the confluent hypergeometric function in. Confluent hypergeometric kummer u function matlab kummeru. Chgu computes the confluent hypergeometric function ua,b,x. The following matlab project contains the source code and matlab examples used for confluent hypergeometric function kummer function. Dataplot uses mz,a,b to be more consistent with how other functions are entered. Download fulltext pdf fortran subroutines for the evaluation of the confluent hypergeometric functions article pdf available august 1989 with 126 reads.
Investigation of harbor oscillations originated from the. The confluent hypergeometric function with special. Fn, a fortran90 library which evaluates elementary and special functions using chebyshev polynomials, including airy, bessel i, bessel j, bessel k, bessel y. In this course we will study multivariate hypergeometric functions in the sense of gelfand, kapranov, and zelevinsky gkz systems. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. There is another important class of paraxial wave modes in cylindrical coordinates in which the complex amplitude is proportional to a confluent hypergeometric function. Confluent hypergeometric function kummer function file. The methods that we investigate include taylor and asymptotic series.
If the real parts of z and a are positive values, then the integral representations of the kummer u function is as follows. The kummer function, as it is also named, belongs to an important class of special functions with a large number of applications in different branches of applied mathematics and physics see and references. Confluent hypergeometric function of the second kind. Properties of matrix variate confluent hypergeometric. On the expansion of confluent hypergeometric functions in. It can be downloaded freely, but i understand it is a shareware product. Dataplot only computes this function for real values. Chguit computes the hypergeometric function using gausslegendre integration. An accurate fortran code for computing hydrogenic continuum wave functions at a wide range of parameters. By specialization of some quantities, there is obtained an expansion in series of modified bessel functions of the first kind, ivz, where v. On the expansion of confluent hypergeometric functions in terms of bessel functions n. The confluent hypergeometric function springerlink.
In this case, the hypergeometric function can be defined as the analytic continuation of the customarily undefined hypergeometric series through a contour integral see dlmf 16. Three lectures on hypergeometric functions eduardo cattani abstract. Fortran subroutines for the evaluation of the confluent. The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity. The two most commonly used hypergeometric functions are the confluent hypergeometric function and the gauss hypergeometric function. This function is largely based at fortran library of special functions which was converted to matlab. The confluent hypergeometric function is a degenerate form the hypergeometric function which arises as a solution the confluent hypergeometric differential equation. Looking forward for your suggestions in this regard. Calculates a specific characteristic value of mathieu functions using subroutine cva1 compute the confluent hypergeometric function ma,b,x using subroutine.
Kummercomplexa,b,z is the confluent hypergeometric function 1f1 kummer function for complex parameters a, b and complex variable z. Acknowledgment the tables of the confluent hypergeometric function have been computed by. A new fortran 90 program to compute regular and irregular associated legendre functions article in computer physics communications 18112. Confluent hypergeometric function projects and source code. The term confluent refers to the merging of singular points of families of differential equations. Calculate airy functions and their first derivatives using subroutine. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. This paper presents a study for investigating and identifying features of oscillation patterns induced by vessel motions in the context of statistical. Special functions of mathematics for engineers pm49sc.
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