Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points

✍ Scribed by W. Eberhard; G. Freiling; A. Schneider

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 929 KB
• Volume: 165
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19941650114

✦ Synopsis

Abstract

We consider the differential equation
on a finite interval I, where I contains m turning points, that is here, zeros of ϕ. Using asymptotic estimates proved by R. E. LANGER for solutions of (*) for intervals containing only one turning point we derive asymptotic estimates (for ρ → ) for a special fundamental system of solutions of (*) in I. The results obtained are fundamental for the investigation of eigenvalue problems defined by (*) and suitable boundary conditions.