Abstract
In this paper, we consider the generalized confluent hypergeometric differential equations of the second order. We shall show that the Borel transforms of formal solutions to these equations can be represented by the hypergeometric functions and that the coefficients of resurgent equations of those differential equations can be calculated explicitly by using connection formulae of the hypergeometric differential equations. Moreover, we shall show that the Stokes multipliers are almost equal to the resurgent constants and that the invariants can be calculated explicitly from them. The idea of these calculations are known classically (cf. [7,8,12]). However, the calculations are seen through by using explicitly resurgent equations. It seems that the explicit formula of invariants will be useful for the resurgent calculus in the future.
Dedicated to Professor Yasutaka Sibuya on the occasion of his sixtieth birthday.
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Majima, H. (1991). Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order. In: Kashiwara, M., Miwa, T. (eds) ICM-90 Satellite Conference Proceedings. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68170-0_11
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DOI: https://doi.org/10.1007/978-4-431-68170-0_11
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