Fungsi hipergeometris

Dalam matematika, fungsi hipergeometris biasa atau Gaussia ₂F₁(a,b;c;z) adalah sebuah fungsi istimewa yang diwakili oleh rangkaian hipergeometris, yang meliputi sebagian besar fungsi istimewa lainnya sebagai kasus spesifik atau pembatasan. Fungsi tersebut adalah solusi dari persamaan diferensial biasa (ODE) linear urutan kedua. Setiap ODE liberal urutan kedua dengan tiga titik tinggal reguler dapat bertransformasi menjadi persamaan tersebut.

Referensi

• Andrews, George E.; Askey, Richard & Roy, Ranjan (1999). Special functions. Encyclopedia of Mathematics and its Applications. 71. Cambridge University Press. ISBN 978-0-521-62321-6. MR 1688958. 
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• Beukers, Frits (2002), Gauss' hypergeometric function. (lecture notes reviewing basics, as well as triangle maps and monodromy)
• Olde Daalhuis, Adri B. (2010), "Fungsi hipergeometris", dalam Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN 978-0-521-19225-5, MR 2723248 
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• Heckman, Gerrit & Schlichtkrull, Henrik (1994). Harmonic Analysis and Special Functions on Symmetric Spaces. San Diego: Academic Press. ISBN 0-12-336170-2.  (part 1 treats hypergeometric functions on Lie groups)
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• Klein, Felix (1981). Vorlesungen über die hypergeometrische Funktion. Grundlehren der Mathematischen Wissenschaften (dalam bahasa German). 39. Berlin, New York: Springer-Verlag. ISBN 978-3-540-10455-1. MR 0668700. Pemeliharaan CS1: Bahasa yang tidak diketahui (link)
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• Kummer, Ernst Eduard (1836). "Über die hypergeometrische Reihe $1+{\tfrac {\alpha \cdot \beta }{1\cdot \gamma }}~x+{\tfrac {\alpha (\alpha +1)\beta (\beta +1)}{1\cdot 2\cdot \gamma (\gamma +1)}}x^{2}+{\tfrac {\alpha (\alpha +1)(\alpha +2)\beta (\beta +1)(\beta +2)}{1\cdot 2\cdot 3\cdot \gamma (\gamma +1)(\gamma +2)}}x^{3}+{\mbox{etc.}}$". Journal für die reine und angewandte Mathematik (dalam bahasa German). 15: 39–83, 127–172. ISSN 0075-4102. Pemeliharaan CS1: Bahasa yang tidak diketahui (link)
• Lavoie, J. L.; Grondin, F.; Rathie, A.K. (1996). "Generalizations of Whipple's theorem on the sum of a ₃F₂". J. Comput. Appl. Math. 72: 293–300. 
• Press, W.H.; Teukolsky, S.A.; Vetterling, W.T. & Flannery, B.P. (2007). "Section 6.13. Hypergeometric Functions". Numerical Recipes: The Art of Scientific Computing (edisi ke-3rd). New York: Cambridge University Press. ISBN 978-0-521-88068-8. 
• Rakha, M.A.; Rathie, Arjun K. (2011). "Extensions of Euler's type-II transformation and Saalschutz's theorem". Bull. Korean Math. Soc. 48 (1): 151–156. 
• Rathie, Arjun K.; Paris, R.B. (2007). "An extension of the Euler's-type transformation for the 3F2 series". Far East J. Math. Sci. 27 (1): 43–48. 
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• Vidunas, Raimundas (2005). "Transformations of some Gauss hypergeometric functions". Journal of Symbolic Computation. 178: 473–487. arXiv:math/0310436 . doi:10.1016/j.cam.2004.09.053. 
• Wall, H.S. (1948). Analytic Theory of Continued Fractions. D. Van Nostrand Company, Inc. 
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• Yoshida, Masaaki (1997). Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces. Braunschweig – Wiesbaden: Friedr. Vieweg & Sohn. ISBN 3-528-06925-2. MR 1453580. 

Pranala luar

• Hazewinkel, Michiel, ed. (2001) [1994], "Hypergeometric function", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4 
• John Pearson, Computation of Hypergeometric Functions (University of Oxford, MSc Thesis)
• Marko Petkovsek, Herbert Wilf and Doron Zeilberger, The book "A = B" (freely downloadable)
• (Inggris) Weisstein, Eric W. "Hypergeometric Function". MathWorld.