TY - JOUR
T1 - A multiple q-exponential differential operational identity
AU - Liu, Zhiguo
N1 - Publisher Copyright:
© 2023, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences.
PY - 2023/11
Y1 - 2023/11
N2 - Using Hartogs’ fundamental theorem for analytic functions in several complex variables and q-partial differential equations, we establish a multiple q-exponential differential formula for analytic functions in several variables. With this identity, we give new proofs of a variety of important classical formulas including Bailey’s 6 ψ 6 series summation formula and the Atakishiyev integral. A new transformation formula for a double q-series with several interesting special cases is given. A new transformation formula for a 3 ψ 3 series is proved.
AB - Using Hartogs’ fundamental theorem for analytic functions in several complex variables and q-partial differential equations, we establish a multiple q-exponential differential formula for analytic functions in several variables. With this identity, we give new proofs of a variety of important classical formulas including Bailey’s 6 ψ 6 series summation formula and the Atakishiyev integral. A new transformation formula for a double q-series with several interesting special cases is given. A new transformation formula for a 3 ψ 3 series is proved.
KW - 05A30
KW - 33D05
KW - 33D15
KW - 33D45
KW - Bailey’s ψ summation
KW - double q-hypergeometric series
KW - q-exponential differential operator
KW - q-hypergeometric series
KW - q-partial differential equation
UR - https://www.scopus.com/pages/publications/85175813592
U2 - 10.1007/s10473-023-0608-3
DO - 10.1007/s10473-023-0608-3
M3 - 文章
AN - SCOPUS:85175813592
SN - 0252-9602
VL - 43
SP - 2449
EP - 2470
JO - Acta Mathematica Scientia
JF - Acta Mathematica Scientia
IS - 6
ER -