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

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=-35/8, b>=a

For fixed z and a=-35/8, b=9/8

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

Input Form

Hypergeometric2F1[-(35/8), 9/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-61636608 + 539561088 z - 2075786955 z^2 + 4548709440 z^3 - 5914484730 z^4 + 8188602508 z^5 - 5909408883 z^6 + 2638542060 z^7 - 677178880 z^8 + 76661760 z^9) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-61636608 + 562674816 z - 2271802203 z^2 + 5275161045 z^3 - 7434596070 z^4 + 2274117778 z^5 - 1587028911 z^6 + 689671353 z^7 - 172888240 z^8 + 19165440 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-61636608 + 539561088 z - 2075786955 z^2 + 4548709440 z^3 - 5914484730 z^4 + 8188602508 z^5 - 5909408883 z^6 + 2638542060 z^7 - 677178880 z^8 + 76661760 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-61636608 + 539561088 z - 2075786955 z^2 + 4548709440 z^3 - 5914484730 z^4 + 8188602508 z^5 - 5909408883 z^6 + 2638542060 z^7 - 677178880 z^8 + 76661760 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (2034613023648975 Pi (1 + Sqrt[1 - z])^(1/4) 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]