Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3vx)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=11/8, b>=a

For fixed z and a=11/8, b=47/8

http://functions.wolfram.com/07.23.03.c3vx.01

Input Form

Hypergeometric2F1[11/8, 47/8, -(21/4), z] == ((1 + Sqrt[1 - z])^(1/4) (2 (52944528 - 713490544 z + 4584957195 z^2 - 19057139578 z^3 + 60317336585 z^4 - 179146263816 z^5 - 1031372213267 z^6 - 40554989970 z^7 + 7130178351 z^8 - 945162780 z^9 + 63693280 z^10) + (1/Sqrt[1 - z]) (105889056 - 1479925616 z + 9870168802 z^2 - 42527481781 z^3 + 138630623476 z^4 - 414365852927 z^5 + 7453142610562 z^6 + 2762005004781 z^7 - 363055790568 z^8 + 62198023383 z^9 - 7911615280 z^10 + 509546240 z^11)))/(211778112 2^(1/4) (-1 + z)^12)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]