The convergence test to the application in a multi-term recurrence relation of a linear ODE

Abstract

The recursive relation starts to appear by putting a function $y(x)={\sum }_{n=0}^{\infty }{d}_n{x}^n$ into a linear ordinary differential equation (ODE). There can be $d$-term of sequences in the recurrence relation of a power series where $d\ge 2$. We discuss the absolute convergence test to the $d$-term recurrence relation with non-constant coefficients of a linear ODE.

arXiv commentmerged with arXiv:1803.03115

References in corpus (1)

• The generalized Heun equation in QFT in curved space-times

Cited by in corpus (1)

• Impossibility of convergence of a Heun function on the boundary of the disc of convergence