Notes on algebraic functions
Consideration of the monodromy group of the hypergeometric equation z(1−z)w″+[γ−(1+α+β)z]w′−αβw=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 give...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203110186 |
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| Summary: | Consideration of the monodromy group of the hypergeometric equation z(1−z)w″+[γ−(1+α+β)z]w′−αβw=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. |
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| ISSN: | 0161-1712 1687-0425 |