An Expression for the Superposition of General Algebraic Functions in Terms of Hypergeometric Series
- 39 Downloads
We show that the superposition of general algebraic functions is representable as a ratio of hypergeometric series.
algebraic function hypergeometric series Mellin transform superposition multidimensional residue
Unable to display preview. Download preview PDF.
- 1.Mellin H. J., “Resolution de l'equation algebrique generale a l'aide de la fonction,” C. R. Acad. Sci., 172, 658–661 (1921).Google Scholar
- 2.Passare M., Tsikh A., and Zhdanov O., “A multidimensional Jordan residue lemma with an application to Mellin-Barnes integrals,” Aspects Math., E 26, 233–241 (1994).Google Scholar
- 3.Zhdanov O. N. and Tsikh A. K., “Studying the multiple Mellin-Barnes integrals by means of multidimensional residues,” Sibirsk. Mat. Zh., 39, No. 2, 282–298 (1998).Google Scholar
- 4.Semusheva A. Yu. and Tsikh A. K., “Continuation of the Mellin studies about solutions of algebraic equations,” in: Complex Analysis and Deferential Operators [in Russian], Krasnoyarsk Univ., Krasnoyarsk, 2000, pp. 134–146.Google Scholar
- 5.Sadykov T. M., “On the Horn system of partial deferential equations and series of hypergeometric type,” Math. Scand., 91, 127–149 (2002).Google Scholar
- 6.Gel'fand I. M., Graev M. I., and Retakh V. S., “General hypergeometric systems of equations and series of hypergeometric type,” Uspekhi Mat. Nauk, 47, No. 4, 3–82 (1992).Google Scholar
- 7.Arnol'd V. I., “Topological invariants of algebraic functions. II,” Funktsional. Anal. i Prilozhen., 4, No. 4, 1–9 (1970).Google Scholar
- 8.Sturmfels B., “Solving algebraic equations in terms of \(A\)-hypergeometric series,” Discrete Math., 15, No. 1-3, 171–181 (2000).Google Scholar
- 9.Gradshte?n I. S. and Ryzhik I. M., Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).Google Scholar
© Plenum Publishing Corporation 2003