지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
Fox \cite{Fox} presented an interesting identity for ${}_pF_q$ which is expressed in terms of a finite summation of ${}_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox \cite{Fox} found a very interesting and general summation formula for ${}_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for ${}_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$ {}_{3}F_{2} \left[ \aligned \alpha,\, \beta,\,\gamma &;\\ \alpha-m,\, \frac{1}{2}(\beta+\gamma+i+1) &; \endaligned \,\, \frac{1}{2} \right],$$ $m$ being a nonnegative integer and $i$ any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for ${}_2F_1(1/2)$ obtained recently by Rakha and Rathie \cite{Ra-Ra}. Several known results are also seen to be certain special cases of our main identities.
목차
등록된 정보가 없습니다.
참고문헌 (9)
참고문헌 신청
A. K. Rathie / 2008 / New summation formula for 3F2(1/2) and Kummer-type II transformation / Math. Commun 13 (1) : 63 ~ 66
C. Fox / 1927 / The expression of hypergeometric series in terms of a similar series / Proc. London Math. Soc 26 : 201 ~ 210
E. D. Rainville / 1960 / Special Functions / Macmillan Company
H. M. Srivastava / 2012 / Zeta and q-Zeta Functions and Associated Series and Integrals / Elsevier Science Publishers
L. J. Slater / 1966 / Generalized Hypergeometric Functions / Cambridge University Press
C. Fox / 1927 / The expression of hypergeometric series in terms of a similar series / Proc. London Math. Soc 26 : 201 ~ 210
E. D. Rainville / 1960 / Special Functions / Macmillan Company
H. M. Srivastava / 2012 / Zeta and q-Zeta Functions and Associated Series and Integrals / Elsevier Science Publishers
L. J. Slater / 1966 / Generalized Hypergeometric Functions / Cambridge University Press
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Certain summation formulas for Humbert's double hypergeometric series $\Psi_2$ and $\Phi_2$
대한수학회논문집
2015 .01
-
ON A NEW CLASS OF SERIES IDENTITIES
호남수학학술지
2015 .01
-
Some summation and Laplace transformation formulas for the Gauss hypergeometric series
Advanced Studies in Contemporary Mathematics
2016 .01
-
NEW LAPLACE TRANSFORMS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION <sub>2</sub>F<sub>2</sub>
호남수학학술지
2015 .01
-
ANOTHER PROOF OF CLASSICAL DIXON'S SUMMATION THEOREM FOR THE SERIES <sub>3</sub>F<sub>2</sub>
호남수학학술지
2019 .01
-
A POWER SERIES ASSOCIATED WITH THE GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE UNIT ARGUMENT WHICH ARE INVOLVED IN BELL POLYNOMIALS
Nonlinear Functional Analysis and Applications
2022 .03
-
EVALUATION OF SOME NEW LAPLACE TRANSFORMS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION <sub>p</sub>F<sub>p</sub>
호남수학학술지
2017 .01
-
On an interesting extension of Kummer's second theorem with applications
대한수학회논문집
2021 .01
-
ON A NEW CLASS OF DOUBLE INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION <sub>3</sub>F<sub>2</sub>
호남수학학술지
2018 .01
-
A note on generalizations of Bailey's identity involving products of generalized hypergeometric series
대한수학회논문집
2022 .04
-
A NOTE ON THREE DERIVATIONS OF GREGORY-LEIBNIZ SERIES FOR π VIA A HYPERGEOMETRIC SERIES APPROACH
East Asian Mathematical Journal
2023 .05
-
$\pi$ and other formulae implied by hypergeometric summation theorems
대한수학회논문집
2015 .01
-
Generalizations of Ramanujan's Integral Associated with Infinite Fourier Cosine Transforms in Terms of Hypergeometric Functions and its Applications
Kyungpook Mathematical Journal
2020 .01
-
Generalized Incomplete Pochhammer Symbols and Their Applications to Hypergeometric functions
Kyungpook Mathematical Journal
2018 .01
-
An Identity Involving Product of Generalized Hypergeometric Series 2F2
Kyungpook Mathematical Journal
2019 .01
-
Extensions of multiple Lauricella and Humbert's confluent hypergeometric functions through a highly generalized Pochhammer symbol and their related properties
대한수학회보
2023 .05
-
A FAMILY OF NEW RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P<sub>n</sub><sup>(</sup><sup>α</sup><sup>,</sup><sup>β</sup><sup>)</sup>(x)
호남수학학술지
2018 .01
-
ON A NEW CLASS OF INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION <sub>3</sub>F<sub>2</sub>
호남수학학술지
2018 .01
-
Generating functions for the extended Wright type hypergeometric function
대한수학회논문집
2017 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0