Special values of fractional hypergeometric functions for function fields

2012 ◽  
Vol 350 (17-18) ◽  
pp. 801-806 ◽  
Author(s):  
Jia-Yan Yao
Keyword(s):  
Hypergeometric Functions ◽  
Function Fields ◽  
Special Values

scholarly journals Explicit logarithmic formulas of special values of hypergeometric functions 3F2

2019 ◽  
Vol 22 (05) ◽  
pp. 1950040
Author(s):  
Masanori Asakura ◽  
Toshifumi Yabu
Keyword(s):  
Linear Combination ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Rational Numbers ◽  
Explicit Description ◽  
Generalized Hypergeometric Function ◽  
Algebraic Numbers ◽  
Nagoya Math ◽  
Special Values ◽  
Geometric Study

In [M. Asakura, N. Otsubo and T. Terasoma, An algebro-geometric study of special values of hypergeometric functions [Formula: see text], to appear in Nagoya Math. J.; https://doi.org/10.1017/nmj.2018.36 ], we proved that the value of [Formula: see text] of the generalized hypergeometric function is a [Formula: see text]-linear combination of log of algebraic numbers if rational numbers [Formula: see text] satisfy a certain condition. In this paper, we present a method to obtain an explicit description of it.

scholarly journals TRANSCENDENCE OF SPECIAL VALUES OF POCHHAMMER FUNCTIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 667-677
Author(s):  
MARVIN D. TRETKOFF ◽  
PAULA TRETKOFF
Keyword(s):  
Hypergeometric Functions ◽  
Higher Order ◽  
Algebraic Numbers ◽  
Special Values

In this paper, we examine the set of algebraic numbers at which higher order hypergeometric functions take algebraic values. In particular, we deduce criteria for this set to be finite and for it to be infinite.

scholarly journals On the Roots of Confluent Hypergeometric Functions

1914 ◽  
Vol 33 ◽  
pp. 48-64 ◽  
Author(s):  
Archd Milne
Keyword(s):  
Hypergeometric Functions ◽  
Graphical Form ◽  
Parabolic Cylinder ◽  
Confluent Hypergeometric Functions ◽  
Special Values ◽  
Parabolic Cylinder Functions ◽  
Class Of Functions

In the present paper the disposition of the roots of the confluent hypergeometric functions — denoted by Wk, m(z) — as affected by changing the parameters k and m is investigated. The results are then shewn in a graphical form, and various typical illustrations of the functions are given. By giving special values to k and m it is then exemplified how the roots of other functions expressible in terms of Wk, m(z) may be studied. The zeros of the parabolic cylinder functions are then discussed. Some of the properties of an allied class of functions, denoted by ψn(z), are then given, and finally, it is shewn how the properties of Abel's function φm(z) may be obtained from results already given.

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