Armenian Journal of Physics=Ֆիզիկայի հայկական հանդես
The cases when the equation for the derivative of the confluent Heun function has only three singularities (in general, the equation has four such points) are examined. It is shown that this occurs only in three specific cases. Further, it is shown that in all these three cases this equation is reduced to some confluent Heun equation with changed parameters. This means that in these cases the derivative of the confluent Heun function is expressed via some other confluent Heun function. The analysis of the obtained relations shows that they can be useful for the construction of some exact solutions of the confluent Heun equation for specific values of involved parameters. Several examples of such cases are presented; and for all the cases the final solutions in terms of simpler special functions are explicitly presented. In addition, it is shown that in the mentioned three cases, the solution can be expanded as a series in terms of generalized hypergeometric functions of Goursat or Clausen.
oai:arar.sci.am:23333
ՀՀ ԳԱԱ Հիմնարար գիտական գրադարան
Dec 13, 2023
Feb 27, 2020
65
https://arar.sci.am/publication/26064
Հրատարակության անուն | Ամսաթիվ |
---|---|
NEW RELATIONS FOR THE DERIVATIVE OF THE CONFLUENT HEUN FUNCTION | Dec 13, 2023 |
T. A. Ishkhanyan V. A. Manukyan A. H. Harutyunyan A. M. Ishkhanyan
V. M. Aroutiounian V. M. Arakelyan E. A. Khachaturyan G. E. Shahnazaryan M. S. Aleksanyan K. M. Gambaryan E. Horvath R. Smajda
Sarian, V. K. Mkrtchyan, A. H. Meshcheryakov, R. V.
V. M. Aroutiounian V. M. Arakelyan M. S. Aleksanyan A. G. Sayunts G. E. Shahnazaryan M. Vrnata P. Fitl J. Viček K. S. Gharajyan H. S. Kasparyan
Aleksanyan, M. S. Aroutiounian, V. M. Shahnazaryan, G. E. Sayunts, A. G.
Д. М. Седракян Д. А. Бадалян Պատ․ խմբ․՝ Գ․ Մ․ Ղարիբյան (1966-1992) Գլխ․ խմբ․՝ Վ․ Մ․ Հարությունյան (1993-2021) Կ․ Մ․ Ղամբարյան (2022-)
Л. А. Оганнесян Г. А. Мурадян А. Ж. Мурадян Պատ․ խմբ․՝ Գ․ Մ․ Ղարիբյան (1966-1992) Գլխ․ խմբ․՝ Վ․ Մ․ Հարությունյան (1993-2021) Կ․ Մ․ Ղամբարյան (2022-)
О. С. Тихова Պատ․ խմբ․՝ Գ․ Մ․ Ղարիբյան (1966-1992) Գլխ․ խմբ․՝ Վ․ Մ․ Հարությունյան (1993-2021) Կ․ Մ․ Ղամբարյան (2022-)