TY - JOUR
T1 - On a Transformation of Triple q-Series and Rogers–Hecke Type Series
AU - Liu, Zhi Guo
N1 - Publisher Copyright:
© 2024, Institute of Mathematics. All rights reserved.
PY - 2024
Y1 - 2024
N2 - Using the method of the q-exponential differential operator, we give an extension of the Sears4 ϕ3 transformation formula. Based on this extended formula and a q-series expansion formula for an analytic function around the origin, we present a transformation formula for triple q-series, which includes several interesting special cases, especially a double q-series summation formula. Some applications of this transformation formula to Rogers– Hecke type series are discussed. More than 100 Rogers–Hecke type identities including Andrews’ identities for the sums of three squares and the sums of three triangular numbers are obtained.
AB - Using the method of the q-exponential differential operator, we give an extension of the Sears4 ϕ3 transformation formula. Based on this extended formula and a q-series expansion formula for an analytic function around the origin, we present a transformation formula for triple q-series, which includes several interesting special cases, especially a double q-series summation formula. Some applications of this transformation formula to Rogers– Hecke type series are discussed. More than 100 Rogers–Hecke type identities including Andrews’ identities for the sums of three squares and the sums of three triangular numbers are obtained.
KW - Rogers–Hecke type series
KW - double q-series summation
KW - q-exponential differential operator
KW - q-partial differential equation
KW - triple q-hypergeomet-ric series
UR - https://www.scopus.com/pages/publications/85207520849
U2 - 10.3842/SIGMA.2024.086
DO - 10.3842/SIGMA.2024.086
M3 - 文章
AN - SCOPUS:85207520849
SN - 1815-0659
VL - 20
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
M1 - 086
ER -