Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bbb2)

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=-37/8, b>=a

For fixed z and a=-37/8, b=-25/8

http://functions.wolfram.com/07.23.03.bbb2.01

Input Form

Hypergeometric2F1[-(37/8), -(25/8), 23/4, z] == (1/(153796489263 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (17168 - 339068 z + 3559141 z^2 - 29416295 z^3 + 304269537 z^4 + 7425434973 z^5 + 14322935391 z^6 + 6641755515 z^7 + 658457739 z^8 - 100533 z^9 + (1/Sqrt[1 - z]) (-17168 + 347652 z - 3726529 z^2 + 31154555 z^3 - 318553313 z^4 - 2470627281 z^5 - 595927455 z^6 + 2444878545 z^7 + 877787109 z^8 + 35086017 z^9 - 402132 z^10)))

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]