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Title
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A Note on the Hypergeometric Mean Value
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Description
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DOI: 10.1007/BF03320978
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Creator
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Richards, Kendall C.
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Date
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2018-02-27
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Date Available
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2018-02-27
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Date Issued
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2001
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Identifier
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Barnard, R. W., & Richards, K. C. (September 01, 2001). A Note on the Hypergeometric Mean Value. Computational Methods and Function Theory, 1, 1, 81-88.
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uri
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https://collections.southwestern.edu/s/suscholar/item/262
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Abstract
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Recent efforts to obtain bounds for the complete elliptic integral 2 ·2F1−1 2, 1 2 ; 1; r2 in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carls considered the approximation of the hypergeometric mean values
( 2F1(−a, b; b + c; r))1/a in terms of means of order t, given by Mt(s, r) :=
{(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is established by first proving a general positivity result involving 3F2.
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Language
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English
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Publisher
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Computational Methods and Function Theory
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Subject
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Hypergeometric function
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Generalized hypergeometric function
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Means of order t
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Type
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Article
