Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6nt)

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=-45/8, b>=a

For fixed z and a=-45/8, b=7/8

http://functions.wolfram.com/07.23.03.b6nt.01

Input Form

Hypergeometric2F1[-(45/8), 7/8, 23/4, z] == (1/(2565092746455 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (257777520 - 2779700924 z + 13710346559 z^2 - 41298622963 z^3 + 89406533970 z^4 - 20182749826 z^5 + 14965740947 z^6 - 7899725567 z^7 + 2784598684 z^8 - 587740160 z^9 + 56218624 z^10 + (1/Sqrt[1 - z]) (-257777520 + 2908589684 z - 15067974831 z^2 + 47822444722 z^3 - 108505714005 z^4 + 140638200464 z^5 - 119681739401 z^6 + 80761015178 z^7 - 39072590371 z^8 + 12736233440 z^9 - 2505561856 z^10 + 224874496 z^11)))

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]