Relevant bibliographies by topics / Gauss hypergeometric functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Gauss hypergeometric functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Gauss hypergeometric functions"

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VIDUNAS, Raimundas. "DEGENERATE GAUSS HYPERGEOMETRIC FUNCTIONS." Kyushu Journal of Mathematics 61, no. 1 (2007): 109–35. http://dx.doi.org/10.2206/kyushujm.61.109.

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VIDUNAS, Raimundas. "DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS." Kyushu Journal of Mathematics 65, no. 1 (2011): 141–67. http://dx.doi.org/10.2206/kyushujm.65.141.

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Chaturvedi, Aparna, and Prakriti Rai. "Some Properties of Extended Hypergeometric Function and Its Transformations." Journal of the Indian Mathematical Society 85, no. 3-4 (2018): 305. http://dx.doi.org/10.18311/jims/2018/20979.

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There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.
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4

ATA, Enes, and İ. Onur KIYMAZ. "Generalized Gamma, Beta and Hypergeometric Functions Defined by Wright Function and Applications to Fractional Differential Equations." Cumhuriyet Science Journal 43, no. 4 (2022): 684–95. http://dx.doi.org/10.17776/csj.1005486.

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When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright function. With the help of generalized beta function, new type of generalized Gauss and confluent hypergeometric functions are obtained. Furthermore, some properties of these functions such as integral representations, derivative formulas, Mellin transforms, Laplace transforms and transform formulas are determined. As examples, we obtained the solutio
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Kumar, Dinesh. "Certain Integrals of Generalized Hypergeometric and Confuent Hypergeometric Functions." Sigmae 5, no. 2 (2016): 8–18. https://doi.org/10.29327/2520355.5.2-2.

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Neste artigo, pretendemos estabelecer certas fórmulas integrais finitas para as funções hipergeométricas generalizadas de Gauss e hipergeométricas confluentes. Além disso, a função $F^{(\alpha ,\beta)}_p(a,b;c;z)$ que ocorre em cada um dos nossos resultados principais pode ser reduzida, em vários casos especiais, a funções mais simples como a clássica Função hipergeométrica de Gauss $_{2}F_{1}$, função hipergeométrica confluente de Gauss $\varphi^{(\alpha ,\beta)}_p(b;c;z)$ função e função hipergeométrica generalizada $_{p} F_{q}$. Um exemplo de algumas dessas aplicações interessantes de nossa
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Nagar, Daya K., Raúl Alejandro Morán-Vásquez, and Arjun K. Gupta. "Properties and Applications of Extended Hypergeometric Functions." Ingeniería y Ciencia 10, no. 19 (2014): 11–31. http://dx.doi.org/10.17230/ingciencia.10.19.1.

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In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions. We also show that these functions occur naturally instatistical distribution theory.
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ABUBAKAR, UMAR MUHAMMAD, and Soraj Patel. "ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS." MALAYSIAN JOURNAL OF COMPUTING 6, no. 2 (2021): 852. http://dx.doi.org/10.24191/mjoc.v6i2.12018.

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Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some of its properties such as symmetric properties, summation formulas, integral representations, connection with some other special functions such as classical beta, error, Mittag – Leffler, incomplete gamma, hypergeometric, classical Wright, Fox – Wright, Fox H and Meijer G – functions. Furthermore, the generalized beta function is used to generalize classical and other exte
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Abdalla, Mohamed, and A. Bakhet. "Extended Gauss Hypergeometric Matrix Functions." Iranian Journal of Science and Technology, Transactions A: Science 42, no. 3 (2017): 1465–70. http://dx.doi.org/10.1007/s40995-017-0183-3.

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Mubeen, Shahid, Gauhar Rahman, Abdur Rehman, and Mammona Naz. "Contiguous Function Relations for k-Hypergeometric Functions." ISRN Mathematical Analysis 2014 (April 10, 2014): 1–6. http://dx.doi.org/10.1155/2014/410801.

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In this research work, our aim is to determine the contiguous function relations for k-hypergeometric functions with one parameter corresponding to Gauss fifteen contiguous function relations for hypergeometric functions and also obtain contiguous function relations for two parameters. Throughout in this research paper, we find out the contiguous function relations for both the cases in terms of a new parameter k>0. Obviously if k→1, then the contiguous function relations for k-hypergeometric functions are Gauss contiguous function relations.
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GUPTA, ARJUN K., and DAYA K. NAGAR. "MATRIX-VARIATE GAUSS HYPERGEOMETRIC DISTRIBUTION." Journal of the Australian Mathematical Society 92, no. 3 (2012): 335–55. http://dx.doi.org/10.1017/s1446788712000353.

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AbstractIn this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric function Φ1of matrix arguments.
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Dissertations / Theses on the topic "Gauss hypergeometric functions"

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Khwaja, Sarah Farid. "Uniform asymptotic approximations of integrals." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/9662.

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In this thesis uniform asymptotic approximations of integrals are discussed. In order to derive these approximations, two well-known methods are used i.e., the saddle point method and the Bleistein method. To start with this, examples are given to demonstrate these two methods and a general idea of how to approach these techniques. The asymptotics of the hypergeometric functions with large parameters are discussed i.e., 2F1 (a + e1λ, b + e2λ c + e3λ ; z)where ej = 0,±1, j = 1, 2, 3 as |λ|→ ∞, which are valid in large regions of the complex z-plane, where a, b and c are fixed. The saddle point
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Khan, Mumtaz Ahmad, and Bhagwat Swaroop Sharma. "A study of three variable analogues of certain fractional integral operators." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95821.

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The paper deals with a three variable analogues of certain fractional integral operators introduced by M. Saigo. Resides giving three variable analogues of earlier known fractional integral operators of one variable as a special cases of newly defined operators, the paper establishes certain results in the form of theorems including integration by parts.
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Kerker, Mohamed Amine. "Sur le problème de Cauchy singulier." Thesis, Reims, 2013. http://www.theses.fr/2013REIMS005.

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L'objet de cette thèse porte sur le problème de Cauchy singulier dans le domaine complexe. Il s'agit d'étudier les singularités de la solution du problème pour trois classes d'équations aux dérivées partielles. Cette thèse s'inscrit dans la continuité des travaux initiés par Jean Leray et son école. Pour décrire les singularités de la solution, on cherche la solution sous la forme d'un développement asymptotique de fonctions hypergéométriques de Gauss. Comme les singularités sont portées par les fonctions hypergéométriques, l'étude de la ramification de la solution se ramène à celle de ces fon
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Books on the topic "Gauss hypergeometric functions"

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Yoshida, Masaaki. Fuchsian differential equations, with special emphasis on the Gauss-Schwarz theory. Vieweg, 1987.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. American Mathematical Society, 2013.

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Tretkoff, Paula. Appell Hypergeometric Functions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0008.

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This chapter discusses the complete quadrilateral line arrangement, and especially its relationship with the space of regular points of the system of partial differential equations defining the Appell hypergeometric function. Appell introduced four series F1, F2, F3, F4 in two complex variables, each of which generalizes the classical Gauss hypergeometric series and satisfies its own system of two linear second order partial differential equations. The solution spaces of the systems corresponding to the series F2, F3, F4 all have dimension 4, whereas that of the system corresponding to the ser
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Tretkoff, Paula. Riemann Surfaces, Coverings, and Hypergeometric Functions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0003.

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This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and notes that an automorphism of a Riemann surface is a biholomorphic map of the Riemann surface onto itself. It then describes a Riemannian metric and the Gauss-Bonnet theorem, which can be interpreted as a relation between the Gaussian curvature of a compact Riemann surface X and its Euler characteristic. It also examines the behavior of the Euler number under finite covering, along with finite subgroup
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Pham, édéric. Singularités des Systèmes Différentiels de Gauss-Manin. Springer London, Limited, 2013.

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Singularités des Systèmes Différentiels de Gauss-Manin. Springer, 2013.

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Tretkoff, Paula, and Hans-Christoph Im Hof. Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.001.0001.

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This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that are free quotients of the complex 2-ball. The book also includes a background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function. The book began as a set of lecture notes, taken by the author, of a course given by Friedrich Hirzebruch at ETH Zürich in 1996. The lecture notes were then considerably expanded over a number
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Book chapters on the topic "Gauss hypergeometric functions"

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Duverney, Daniel. "Gauss Hypergeometric Function." In An Introduction to Hypergeometric Functions. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-65144-1_4.

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Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Gauss Hypergeometric Function F(a,b,c,x)." In An Atlas of Functions. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_61.

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Aomoto, Kazuhiko, and Michitake Kita. "Introduction: the Euler−Gauss Hypergeometric Function." In Springer Monographs in Mathematics. Springer Japan, 2011. http://dx.doi.org/10.1007/978-4-431-53938-4_1.

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Hata, Masayoshi, and Marc Huttner. "Padé Approximation to the Logarithmic Derivative of the Gauss Hypergeometric Function." In Analytic Number Theory. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3621-2_10.

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"A Sets, relations and functions." In Gauss Hypergeometric Function. De Gruyter, 2024. http://dx.doi.org/10.1515/9783111324586-008.

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"6 Extended Gauss hypergeometric functions." In Gauss Hypergeometric Function. De Gruyter, 2024. http://dx.doi.org/10.1515/9783111324586-006.

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Dwork, Bernard. "Multiplication By xu (Gauss Contiguity)." In Generalized hypergeometric functions. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198535676.003.0002.

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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.

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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.
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Faraut, Jacques, and Adam Korányi. "Special Functions." In Analysis on Symmetric Cones. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198534778.003.0015.

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Abstract It is strongly suggested by the generalized binomial expansion of Chapter XII that a multivariable version of the hypergeometric function can be associated with every symmetric cone. The theory of these functions is the subject of the present chapter. After proving some general results we look in more detail at the special cases of generalized Bessel functions and Gauss hypergeometric functions. We establish some connections with spherical functions on the tube TΩ and we prove the generalization of a number of classical results including a rather complete theory of the Hankel transfor
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Srinivasa Rao, K. "Gauss, hypergeometric series, and Ramanujan." In Generalized Hypergeometric Functions: Transformations and group theoretical aspects. IOP Publishing, 2018. http://dx.doi.org/10.1088/978-0-7503-1496-1ch9.

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Conference papers on the topic "Gauss hypergeometric functions"

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Cai, Jianping, Mingming Chen, Shuangyue Zhang, Chengxi Hong, and Yuehong Lu. "A Fast Algorithm for Solving a Kind of Gauss Hypergeometric Functions in Wireless Communication Based on Pfaff Transformation." In 2019 International Conference on Networking and Network Applications (NaNA). IEEE, 2019. http://dx.doi.org/10.1109/nana.2019.00024.

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Sarikaya, Mehmet Zeki. "Hermite-Hadamard inequalities involving the Gauss hypergeometric function." In 7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5078478.

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Hirata-Kohno, Noriko, Marc Huttner, and Takao Komatsu. "Diophantine approximation of the values of hypergeometric function of Gauss." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841896.

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