TY - JOUR

T1 - Asymptotic and numeric study of eigenvalues of the double confluent Heun equation

AU - Lay, W.

AU - Bay, K.

AU - Slavyanov, S. Yu

PY - 1998/10/23

Y1 - 1998/10/23

N2 - The spectrum of the boundary problems related to the double confluent case of Heun's differential equation is studied numerically and by means of asymptotic methods. The calculation is based on an application of the central two-point connection problem for this equation using Jaffé expansions and Birkhoff sets of irregular difference equations of Poincaré-Perron type. The numerical evaluation based on this approach is compared with results of asymptotic calculations showing several quite interesting features of the eigenvalue curves and of the solution of the equation itself.

AB - The spectrum of the boundary problems related to the double confluent case of Heun's differential equation is studied numerically and by means of asymptotic methods. The calculation is based on an application of the central two-point connection problem for this equation using Jaffé expansions and Birkhoff sets of irregular difference equations of Poincaré-Perron type. The numerical evaluation based on this approach is compared with results of asymptotic calculations showing several quite interesting features of the eigenvalue curves and of the solution of the equation itself.

UR - http://www.scopus.com/inward/record.url?scp=0032561109&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/31/42/011

DO - 10.1088/0305-4470/31/42/011

M3 - Article

AN - SCOPUS:0032561109

VL - 31

SP - 8521

EP - 8531

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 42

ER -