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We consider the phase-integral method applied to an arbitrary linear ordinarysecond-order differential equation with non-analytical coefficients. We proposea universal technique based on the Frobenius method which allows to obtain newexact relation between connection matrices associated with its generalsolution. The technique allows the reader to write an exact algebraic equationfor the Stokes constants provided the differential equation has at most oneregular singular point in a finite area of the complex plane. We also propose away to write approximate relations between Stokes constants in case of multipleregular singular points located far away from each other. The well-known Buddenproblem is solved with help of this technique as an illustration of its usage.To access the HTML version of the paper & discuss it with the author, visithttps://enabla.com/pub/607.

On a new exact relation for the connection matrices in case of a linear second-order ODE with non-analytic coefficients