Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7hb)

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=-25/8

http://functions.wolfram.com/07.23.03.b7hb.01

Input Form

Hypergeometric2F1[-(43/8), -(25/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-12681216 + 266652288 z - 2962910313 z^2 + 25301728341 z^3 - 239213788695 z^4 - 15081689980023 z^5 - 36468054389821 z^6 - 21257762943809 z^7 - 2821582650957 z^8 - 2116876125 z^9 + 47570250 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (792576 - 16089912 z + 173547441 z^2 - 1456371945 z^3 - 1671583776975 z^4 - 4529614888497 z^5 - 2864822947301 z^6 - 412625281747 z^7 - 1051302525 z^8 + 23785125 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1585152 - 33071472 z + 365017239 z^2 - 3104442405 z^3 + 2051995643775 z^4 + 6445975329831 z^5 + 5295860548529 z^6 + 1308915390097 z^7 + 70427755125 z^8 - 866729955 z^9 + 19028100 z^10) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-12681216 + 266652288 z - 2962910313 z^2 + 25301728341 z^3 - 239213788695 z^4 - 15081689980023 z^5 - 36468054389821 z^6 - 21257762943809 z^7 - 2821582650957 z^8 - 2116876125 z^9 + 47570250 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (2651043697920542925 Pi z^5)

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]