Tohoku Mathematical Journal
2010
June
SECOND SERIES VOL. 62, NO. 2

Tohoku Math. J.
62 (2010), 263-268

Title A TRANSFORMATION FORMULA FOR APPELL'S HYPERGEOMETRIC FUNCTION $F_1$ AND COMMON LIMITS OF TRIPLE SEQUENCES BY MEAN ITERATIONS

Author Keiji Matsumoto

(Received June 19, 2009, revised January 25, 2010)
Abstract. In this paper, we give a transformation formula for Appell's hypergeometric function $F_1$. As applications of this formula, we show that some common limits of triple sequences given by mean iterations of 3-terms can be expressed by $F_1$.

2000 Mathematics Subject Classification. Primary 26A18; Secondary 33C65.
Key words and phrases. Hypergeometric function, arithmetic-geometric mean, mean iteration.

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