# On the Voros Coefficient for the Whittaker Equation with a Large Parameter – Some Progress around Sato's Conjecture in Exact WKB Analysis

### Tatsuya Koike

Kyoto University, Japan### Yoshitsugu Takei

Kyoto University, Japan

## Abstract

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.

## Cite this article

Tatsuya Koike, Yoshitsugu Takei, 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), no. 1, pp. 375–395

DOI 10.2977/PRIMS/39