Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bx76)

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=-1/8, b>=a

For fixed z and a=-1/8, b=43/8

http://functions.wolfram.com/07.23.03.bx76.01

Input Form

Hypergeometric2F1[-(1/8), 43/8, -(21/4), z] == (2987712 (1 + Sqrt[1 - z]) - 35568 (887 + 845 Sqrt[1 - z]) z + 17784 (8457 + 7633 Sqrt[1 - z]) z^2 - 513 (829877 + 704531 Sqrt[1 - z]) z^3 + 285 (2766913 + 2186191 Sqrt[1 - z]) z^4 - 3990 (244725 + 176117 Sqrt[1 - z]) z^5 + 48586230 (11 + 5 Sqrt[1 - z]) z^6 - 2255 (219631 + 67649 Sqrt[1 - z]) z^7 + 2255 (120327 + 26681 Sqrt[1 - z]) z^8 - 12300 (7797 + 1124 Sqrt[1 - z]) z^9 + 52480 (382 + 27 Sqrt[1 - z]) z^10 - 1889280 z^11)/ (2987712 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1 - z)^(21/2))

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]