Log in

Relevant bibliographies by topics / Hypergeometric Kummer's function

Contents

Journal articles
Book chapters

Academic literature on the topic 'Hypergeometric Kummer's function'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Hypergeometric Kummer's function.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Hypergeometric Kummer's function"

1

Qureshi, M. I., M. Sadiq Khan, M. A. Pathan, and N. U. Khan. "Some multivariable Gaussian hypergeometric extensions of the Preece theorem." ANZIAM Journal 48, no. 1 (2006): 143–50. http://dx.doi.org/10.1017/s1446181100003473.

Full text

Abstract:

AbstractSome generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric function and Srivastava's quadruple hypergeometric function F(4) and triple hypergeometric function F(3). Some known results of Preece, Pathan and Bailey are also obtained as special cases.

APA, Harvard, Vancouver, ISO, and other styles

2

Milovanovic, Gradimir, Rakesh Parmar, and Arjun Rathie. "A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1." Applicable Analysis and Discrete Mathematics 12, no. 1 (2018): 257–72. http://dx.doi.org/10.2298/aadm171017002m.

Full text

Abstract:

Motivated by recent generalizations of classical theorems for the series 2F1 [Integral Transform. Spec. Funct. 229(11), (2011), 823-840] and interesting Laplace transforms of Kummer's confluent hypergeometric functions obtained by Kim et al. [Math. Comput. Modelling 55 (2012), 1068-1071], first we express generalized summations theorems in explicit forms and then by employing these, we derive various new and useful Laplace transforms of convolution type integrals by using product theorem of the Laplace transforms for a pair of Kummer's confluent hypergeometric function.

APA, Harvard, Vancouver, ISO, and other styles

3

Mathews, W. N., M. A. Esrick, Z. Y. Teoh, and J. K. Freericks. "A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions." Condensed Matter Physics 25, no. 3 (2022): 33203. http://dx.doi.org/10.5488/cmp.25.33203.

Full text

Abstract:

The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are the Kummer function, M(a,b,z), often referred to as the confluent hypergeometric function of the first kind, and M ≡ z1-bM(1+a-b, 2-b,z), where a and b are parameters that appear in the differential equation. A third function, the Tricomi function, U(a,b,z), sometimes referred to as the confluent hypergeometric function of the second kind, is also a solution of the confluent hypergeometric equation

APA, Harvard, Vancouver, ISO, and other styles

4

Morita, Tohru. "Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Nonstandard Analysis, in Terms of the Green's Function." Journal of Advances in Mathematics and Computer Science 39, no. 1 (2024): 20–28. http://dx.doi.org/10.9734/jamcs/2024/v39i11859.

Full text

Abstract:

Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green's function. In a preceding paper, solution is given without using the Green's function, on the basis of nonstandard analysis, for a restricted class of inhomogeneous terms. In the present paper, the corresponding solutions are given in terms of the Green's function. It is applied to Kummer's and the hypergeometric differential equation.

APA, Harvard, Vancouver, ISO, and other styles

5

Mohammed, Asmaa Orabi, Medhat A. Rakha, Mohammed M. Awad, and Arjun K. Rathie. "On several new Laplace transforms of generalized hypergeometric functions 2F2(x)." Boletim da Sociedade Paranaense de Matemática 39, no. 4 (2021): 97–109. http://dx.doi.org/10.5269/bspm.42207.

Full text

Abstract:

By employing generalizations of Gauss's second, Bailey's and Kummer's summation theorems obtained earlier by Rakha and Rathie, we aim to establish unknown Laplace transform of six rather general formulas of generalized hypergeometric function 2F2[a,b;c,d;x]. The results obtained in this paper are simple, interesting, easily established and may be useful in theoretical physics, engineering and mathematics. Results obtained earlier by Kim et al. and Choi and Rathie follow special cases of our main findings.

APA, Harvard, Vancouver, ISO, and other styles

6

Moothathu, T. S. K. "The Best Estimators of Quantiles and the Three Means of the Pareto Distribution." Calcutta Statistical Association Bulletin 35, no. 3-4 (1986): 111–22. http://dx.doi.org/10.1177/0008068319860301.

Full text

Abstract:

In this paper we develop the uniformly minimum variance unbiased (best) estimators of the quantiles, mean, geometric mean and harmonic mean of the Pareto distribuion in the case when both the shape parameter a and the scale parameter k are unknown and in cases when one of them alone is unknown. The best estimates are in terms of the Bessel Function o F1 and Kummer's function 1 F1. The variance of the best estimator are found out, which are in terms of F2 , the Appell function of second kind and ψ2 , a confluent hypergeometric function of two variables. Further we prove that every best estimato

APA, Harvard, Vancouver, ISO, and other styles

7

Guillemin, Fabrice, and Didier Pinchon. "Continued Fraction Analysis of the Duration of an Excursion in an M/M/∞ System." Journal of Applied Probability 35, no. 1 (1998): 165–83. http://dx.doi.org/10.1239/jap/1032192560.

Full text

Abstract:

We show in this paper how the Laplace transform θ* of the duration θ of an excursion by the occupation process {Λt} of an M/M/∞ system above a given threshold can be obtained by means of continued fraction analysis. The representation of θ* by a continued fraction is established and the [m−1/m] Padé approximants are computed by means of well known orthogonal polynomials, namely associated Charlier polynomials. It turns out that the continued fraction considered is an S fraction and as a consequence the Stieltjes transform of some spectral measure. Then, using classic asymptotic expansion prope

APA, Harvard, Vancouver, ISO, and other styles

8

Guillemin, Fabrice, and Didier Pinchon. "Continued Fraction Analysis of the Duration of an Excursion in an M/M/∞ System." Journal of Applied Probability 35, no. 01 (1998): 165–83. http://dx.doi.org/10.1017/s0021900200014765.

Full text

Abstract:

We show in this paper how the Laplace transform θ* of the duration θ of an excursion by the occupation process {Λ t } of an M/M/∞ system above a given threshold can be obtained by means of continued fraction analysis. The representation of θ* by a continued fraction is established and the [m−1/m] Padé approximants are computed by means of well known orthogonal polynomials, namely associated Charlier polynomials. It turns out that the continued fraction considered is an S fraction and as a consequence the Stieltjes transform of some spectral measure. Then, using classic asymptotic expansion pro

APA, Harvard, Vancouver, ISO, and other styles

9

Poudel, Madhav Prasad, Harsh Vardhan Harsh, Narayan Prasad Pahari, and Dinesh Panthi. "Kummer’s Theorems, Popular Solutions and Connecting Formulas on Hypergeometric Function." Journal of Nepal Mathematical Society 6, no. 1 (2023): 48–56. http://dx.doi.org/10.3126/jnms.v6i1.57413.

Full text

Abstract:

The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ +b−1)−z(θ +a)]w = 0. Kummer’s first formula and Kummer’s second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensiv

APA, Harvard, Vancouver, ISO, and other styles

10

Yuriy, Khomyak, Naumenko Ievgeniia, Zheglova Victoriia, and Popov Vadim. "MINIMIZING THE MASS OF A FLAT BOTTOM OF CYLINDRICAL APPARATUS." Eastern-European Journal of Enterprise Technologies 2, no. 1 (92) (2018): 42–50. https://doi.org/10.15587/1729-4061.2018.126141.

Full text

Abstract:

In the bodies of cylindrical apparatuses that operate under pressure, one of the weak elements is a flat bottom whose thickness is increased by 4…5 times in comparison with the wall thickness. This is due to the fact that the bottom is exposed to a more unfavorable bending deformation compared to the wall that «works» on stretching. In order to reduce specific metal consumption for the bottom, we propose the optimization of the shape of a radial cross-section by a rational redistribution of the material: to increase thickness of the bottom in the region of its contact w

APA, Harvard, Vancouver, ISO, and other styles

More sources

Book chapters on the topic "Hypergeometric Kummer's function"

1

Duverney, Daniel. "Kummer Hypergeometric Function." In An Introduction to Hypergeometric Functions. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-65144-1_6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Takayama, Nobuki. "Generating Kummer Type Formulas for Hypergeometric Functions." In Algebra, Geometry and Software Systems. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05148-1_7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Andrews, Larry C. "The Confluent Hypergeometric Functions." In Special Functions Of Mathematics For Engineers. Oxford University PressOxford, 1998. http://dx.doi.org/10.1093/oso/9780198565581.003.0010.

Full text

Abstract:

Abstract Whereas Gauss was largely responsible for the systematic study of the hypergeometric function, E. E. Kummer (1810-1893) is the person most associated with developing properties of the related confluent hypergeometric function. Kummer published his work on this function in 1836,* and since that time it has been commonly referred to as Kummer’s function. Like the hypergeometric function, the confluent hypergeometric function is related to a large number of other functions.

APA, Harvard, Vancouver, ISO, and other styles

4

Yang, Xiao-Jun. "Hypergeometric supertrigonometric and superhyperbolic functions via Kummer confluent hypergeometric series." In An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions. Elsevier, 2021. http://dx.doi.org/10.1016/b978-0-12-824154-7.00010-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Srinivasa Rao, K. "Group theory of the Kummer solutions of the Gauss differential equation." In Generalized Hypergeometric Functions: Transformations and group theoretical aspects. IOP Publishing, 2018. http://dx.doi.org/10.1088/978-0-7503-1496-1ch3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!