Contiguous relations and their computations for 2F1 hypergeometric series

Adel K. Ibrahim, Medhat A. Rakha*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمقالمراجعة النظراء

12 اقتباسات (Scopus)


The hypergeometric function 2F1 [a1, a2 ; a3 ; z] plays an important role in mathematical analysis and its application. Gauss defined two hypergeometric functions to be contiguous if they have the same power-series variable, if two of the parameters are pairwise equal, and if the third pair differs by ±1. He showed that a hypergeometric function and any two other contiguous to it are linearly related. In this paper, we present an interesting formula as a linear relation of three shifted Gauss polynomials in the three parameters a1, a2 and a3. More precisely, we obtained a recurrence relation including 2F1 [a1 + α1, a2 ; a3 ; z], 2F1 [a1, a2 + α2 ; a3 ; z] and 2F1 [a1, a2 ; a3 + α3 ; z] for any arbitrary integers α1, α2 and α3.

اللغة الأصليةEnglish
الصفحات (من إلى)1918-1926
عدد الصفحات9
دوريةComputers and Mathematics with Applications
مستوى الصوت56
رقم الإصدار8
المعرِّفات الرقمية للأشياء
حالة النشرPublished - أكتوبر 2008
منشور خارجيًانعم

ASJC Scopus subject areas

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