Abstract
Using the theory of functions of several variables and q-calculus, we prove an expansion theorem for the analytic function in several variables which satisfies a system of q-partial differential equations. Some curious applications of this expansion theorem to q-series are discussed. In particular, an extension of Andrews’ transformation formula for the q-Lauricella function is given.
This paper is dedicated to Professor Krishnaswami Alladi on the occasion of his 60th birthday
This work was supported by the National Natural Science Foundation of China (Grant No. 11571114) and Science and Technology Commission of Shanghai Municipality (Grant No. 13dz2260400).
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Acknowledgements
I am grateful to the anonymous referee for careful reading of the manuscript and many invaluable suggestions and comments.
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Liu, ZG. (2017). On a System of q-Partial Differential Equations with Applications to q-Series. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_25
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