# Publications of the Research Institute for Mathematical Sciences

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**Volume 47, Issue 1, 2011, pp. 375–395**

**DOI: 10.2977/PRIMS/39**

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 Analysis

Tatsuya Koike^{[1]}and Yoshitsugu Takei

^{[2]}(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