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- W2912963984 abstract "In 1915, Ramanujan stated the following formula ∫ 0 ∞ t x - 1 ( - a t ; q ) ∞ ( - t ; q ) ∞ d t = π sin π x ( q 1 - x , a ; q ) ∞ ( q , a q - x ; q ) ∞ , where 0 < q < 1 , x > 0 , and 0 < a < q x . The above formula is called Ramanujan’s beta integral. In this paper, by using q-exponential operator, we further extend Ramanujan’s beta integral. As some applications, we obtain some new integral formulas of Ramanujan and also show some new representation with gamma functions and q-gamma functions." @default.
- W2912963984 created "2019-02-21" @default.
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- W2912963984 date "2019-01-23" @default.
- W2912963984 modified "2023-09-25" @default.
- W2912963984 title "A Further Extension for Ramanujan’s Beta Integral and Applications" @default.
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- W2912963984 doi "https://doi.org/10.3390/math7020118" @default.
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