Publications of the Research Institute for Mathematical Sciences
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Published online: 2011-03-24
On the Voros Coefficient for the Whittaker Equation with a Large Parameter – Some Progress around Sato's Conjecture in Exact WKB AnalysisTatsuya Koike and Yoshitsugu Takei (1) Kyoto University, Japan
(2) Kyoto University, Japan
Generalizing Sato's conjecture for the Weber equation in exact WKB analysis, we explicitly determine the Voros coefficient of the Whittaker equation with a large parameter. By using our results we also compute alien derivatives of WKB solutions of the Whittaker equation at the so-called xed singular points of their Borel transform.
Keywords: exact WKB analysis, Whittaker equation, Voros coefficient, alien derivative, Stokes automorphism
Koike Tatsuya, Takei Yoshitsugu: On the Voros Coefficient for the Whittaker Equation with a Large Parameter – Some Progress around Sato's Conjecture in Exact WKB Analysis. Publ. Res. Inst. Math. Sci. 47 (2011), 375-395. doi: 10.2977/PRIMS/39