Notes on algebraic functions

Guan Ke-Ying and Lei Jinzhi

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

Consideration of the monodromy group of the hypergeometric equation z ( 1 − z ) w ″ + [ γ − ( 1 + α + β ) z ] w ′ − α β w = 0 , in the case of α = 1 / 6 , β = 5 / 6 , γ = 7 / 6 , shows that the global hypergeometric function solution F ( 1 / 6 ; 5 / 6 ; 7 / 6 ; z ) is nonalgebraic although it has only algebraic singularities. Therefore, the proposition given in [2,4] that a function is algebraic if it has only the algebraic singularities on the extended z -plane is not true. Through introduction of the concept of singular element criterion for deciding when a function is algebraic on the basis of properties of its singularities is given.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:794709

DOI: 10.1155/S0161171203110186

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