On the solutions of the biconfluent Heun equations (Q1420711)

Here, the biconfluent Heun equation \[ xu''(x)+(1+\alpha-\beta x-2x^{2})u'(x)+{(\gamma-\alpha-2)x-\frac{1}{2}(\delta+(\alpha+1)\beta)}u(x)=0 \] where \(\alpha, \beta, \gamma, \delta \in \mathbb{C}\) is discussed. The singularity is regular at \(0\) and irregular at \(\infty\). By using \(k\)-summability (see for definitions and references \textit{J. Martinet and J.-P. Ramis} [Ann. Inst. Henri Poincaré, 5, No. 4, 331--401 (1991; Zbl 0748.12005)]), he obtains new integral formulas for bases of solutions near \(\infty\).