Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9kb)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9kb.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, 23/4, z] == (16 2^(3/4) (-4 (230010 + 421685 z + 1083835 z^2 + 4140180 z^3 - 1169352847 z^4 + 5287914193 z^5 - 9788870208 z^6 + 9175751936 z^7 - 4337795072 z^8 + 825556992 z^9) + (1/Sqrt[1 - z]) (920040 + 1226720 z + 3376965 z^2 + 14124705 z^3 + 4934991223 z^4 - 29220423861 z^5 + 71520066192 z^6 - 93312737024 z^7 + 68551262208 z^8 - 26895777792 z^9 + 4402970624 z^10)))/ (153941859981 (1 + Sqrt[1 - z])^(3/4) z^4)

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]