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Dergiler / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 5

A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications

Mohammad Idris QURESHI
Shakir Hussain MALIK
Richard Bruce PARIS
Sayfa
1903–1913
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We derive a summation formula for the terminating hypergeometric series 4F3 [ −m, a, b, 1 + c 1 + a + m, 1 + a − b, c ; 1] , where m denotes a nonnegative integer.
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Temel Bulgular & Veri:Special cases of this reduction formula lead to several reduction formulas for the hypergeometric functions p+1Fp with quadratic arguments when p = 2, 3 and 4 by employing series rearrangement techniques.
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Sonuç & Katkı:A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We derive a summation formula for the terminating hypergeometric series 4F3 [ −m, a, b, 1 + c 1 + a + m, 1 + a − b, c ; 1] , where m denotes a nonnegative integer. Using this summation formula, we establish a reduction formula for the Srivastava–Daoust double hypergeometric function with arguments z and −z . Special cases of this reduction formula lead to several reduction formulas for the hypergeometric functions p+1Fp with quadratic arguments when p = 2, 3 and 4 by employing series rearrangement techniques. A general double series identity involving a bounded sequence of arbitrary complex numbers is also given.

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Bu Makaleye Atıf Yap

QURESHI, M. I., MALIK, S. H., PARIS, R. B. (2022). A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 5, 1903–1913. https://ajindex.com/articles/607364

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Kaynakça (6)

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