Intégrales hyperelliptiques (mais pas hypergéométriques) satisfaisant à des équations différentielles du second ordre

Investigation of an innocent generating function of the squares of Legendre polynomials has brought to life an interesting family of (Apéry type) second order linear differential equations whose solutions are hyperelliptic integrals, which cannot be expressed in terms of elementary and hypergeometric functions.

The talk is based on joint work with Mark van Hoeij and Duco van Straten; it will be delivered in English.