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On the finite sum representations and transcendence properties of the Lauricella functions

โœ Scribed by Ping Zhou

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
209 KB
Volume
236
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

We first generalize the results in Tan and Zhou (2005) [2] that a Lauricella function

variables can be written as a finite sum of rational functions and logarithm functions of one variable, for a, b 1 , . . . , b n , c positive integers with c โ‰ฅ a + 1, and for distinct x 1 , . . . , x n , to all x 1 , . . . , x n not necessarily distinct. Then we use the finite sum representation to prove that the values of F D (a, b 1 , . . . , b n ; c; x 1 , . . . , x n ), for positive integers a, b 1 , . . . , b n , c with c > a, and real algebraic numbers x 1 , . . . , x n with 0 < x 1 , . . . , x n < 1, are transcendental.

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