Generalization of a Quadratic Transformation Formula due to Gauss
The aim of this research paper is to obtain explicit expressions of (1−𝑥)2−2𝑎𝐹1[𝑎,𝑏;−4𝑥/(1−𝑥)22𝑏+𝑗]for 𝑗=0,±1,±2. For 𝑗=0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follo...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/789519 |
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| author | Medhat A. Rakha |
| author_facet | Medhat A. Rakha |
| author_sort | Medhat A. Rakha |
| collection | DOAJ |
| description | The aim of this research paper is to obtain explicit expressions of (1−𝑥)2−2𝑎𝐹1[𝑎,𝑏;−4𝑥/(1−𝑥)22𝑏+𝑗]for 𝑗=0,±1,±2. For 𝑗=0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings. |
| format | Article |
| id | doaj-art-a38d91d351e64bb8b0271d021237f7d2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a38d91d351e64bb8b0271d021237f7d22025-08-20T03:38:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/789519789519Generalization of a Quadratic Transformation Formula due to GaussMedhat A. Rakha0Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Alkhodh, Muscat 123, OmanThe aim of this research paper is to obtain explicit expressions of (1−𝑥)2−2𝑎𝐹1[𝑎,𝑏;−4𝑥/(1−𝑥)22𝑏+𝑗]for 𝑗=0,±1,±2. For 𝑗=0, we have the well-known transformation formula due to Gauss. The results are derived with the help of generalized Watson's theorem. Some known results obtained earlier follow special cases of our main findings.http://dx.doi.org/10.1155/2012/789519 |
| spellingShingle | Medhat A. Rakha Generalization of a Quadratic Transformation Formula due to Gauss International Journal of Mathematics and Mathematical Sciences |
| title | Generalization of a Quadratic Transformation Formula due to Gauss |
| title_full | Generalization of a Quadratic Transformation Formula due to Gauss |
| title_fullStr | Generalization of a Quadratic Transformation Formula due to Gauss |
| title_full_unstemmed | Generalization of a Quadratic Transformation Formula due to Gauss |
| title_short | Generalization of a Quadratic Transformation Formula due to Gauss |
| title_sort | generalization of a quadratic transformation formula due to gauss |
| url | http://dx.doi.org/10.1155/2012/789519 |
| work_keys_str_mv | AT medhatarakha generalizationofaquadratictransformationformuladuetogauss |