CONVERGENCE OF GAUSS CONTINUED FRACTION FOR THE RATIO OF HYPERGEOMETRIC FUNCTIONS IN Qp
Keywords:
hypergeometric functions of Gauss, continued fraction of Gauss, p-adic numbers.Abstract
The conditions of convergence of Gauss continued fraction to the ratio of hypergeometric functions in the field of p-adic numbers are established.
References
1. Gauss C. F. Disquisitiones Generales circa Seriem Infinitam Pars prior, Comm. soc. regiae sci. Gottingensis rec. 2 (1812), 1-46, Werke; Band 3, Königliche Gesellschaft der Wissenschaften, Göttingen (1876), 123-162.
2. Lorentzen L. Continued fractions with applications / L.Lorentzen, H.Waadeland // Vol. 3 of Studies in Computational Mathematics. – North-Holland Publishing Co., Amsterdam, 1992.
3. Jones W.B. Continued Fractions. Analytic Theory and Applications / W.B.Jones, W.J.Thron // Vol. 11 of Encyclopedia of Mathematics and its Applications. Addison-Wesley Publishing Co., Reading, Mass., 1980.
4. Koblitz N. p-adic Numbers, p-adic Analysis, and Zeta-Functions, N.Koblitz / Graduate Texts in Mathematics. – No. 58, Springer-Verlag, New York, 1977. Second edition, 1984.
2. Lorentzen L. Continued fractions with applications / L.Lorentzen, H.Waadeland // Vol. 3 of Studies in Computational Mathematics. – North-Holland Publishing Co., Amsterdam, 1992.
3. Jones W.B. Continued Fractions. Analytic Theory and Applications / W.B.Jones, W.J.Thron // Vol. 11 of Encyclopedia of Mathematics and its Applications. Addison-Wesley Publishing Co., Reading, Mass., 1980.
4. Koblitz N. p-adic Numbers, p-adic Analysis, and Zeta-Functions, N.Koblitz / Graduate Texts in Mathematics. – No. 58, Springer-Verlag, New York, 1977. Second edition, 1984.
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Published
2019-02-19
How to Cite
Симотюк, М. М., & Медвідь, О. М. (2019). CONVERGENCE OF GAUSS CONTINUED FRACTION FOR THE RATIO OF HYPERGEOMETRIC FUNCTIONS IN Qp. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(33), 110–117. Retrieved from https://pvntsh.nung.edu.ua/index.php/number/article/view/107
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Section
Mathematics and Mechanics
