We prove a Fredholm determinant and short-distance series representation of the Painlevé V tau function associated with generic monodromy data. Using a relation of to two different types of irregular c = 1 Virasoro conformal blocks and the confluence from Painlevé VI equation, connection formulas between the parameters of asymptotic expansions at 0 and i∞ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as t → 0, +∞, i∞ are obtained. We also show that irregular conformal blocks of rank 1, for arbitrary central charge, are obtained as confluent limits of the regular conformal blocks.
Skip Nav Destination
Research Article| August 30 2018
Irregular conformal blocks and connection formulae for Painlevé V functions
Special Collection: In Memory of Ludwig Faddeev
H. Nagoya ;
O. Lisovyy, H. Nagoya, J. Roussillon; Irregular conformal blocks and connection formulae for Painlevé V functions. J. Math. Phys. 1 September 2018; 59 (9): 091409. https://doi.org/10.1063/1.5031841
Download citation file: