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

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=43/8, b>=a

For fixed z and a=43/8, b=47/8

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

Input Form

Hypergeometric2F1[43/8, 47/8, -(17/4), z] == (1/(219232 2^(1/4) (-1 + z)^15)) ((1 + Sqrt[1 - z])^(1/4) (-109616 + 2451852 z - 29067491 z^2 + 263256805 z^3 - 2492192703 z^4 - 116065239631 z^5 - 298706731785 z^6 - 203665590513 z^7 - 39452182245 z^8 - 1547993713 z^9 + (1/Sqrt[1 - z]) (-109616 + 2506660 z - 30279715 z^2 + 277490920 z^3 - 2620336628 z^4 + 259901837536 z^5 + 1015041778542 z^6 + 1025801324856 z^7 + 321367794300 z^8 + 26764475612 z^9 + 267113693 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]