Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8oq)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-35/8

http://functions.wolfram.com/07.23.03.b8oq.01

Input Form

Hypergeometric2F1[-(41/8), -(35/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (14778368 - 350004864 z + 4450656969 z^2 - 44406942888 z^3 + 504555212700 z^4 + 40627112186664 z^5 + 132470862070038 z^6 + 117831555753192 z^7 + 32254039533276 z^8 + 2205513645720 z^9 + 11190567465 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 80 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (115456 - 2715471 z + 34331022 z^2 - 341429550 z^3 + 337431367350 z^4 + 1382060661588 z^5 + 1605941437962 z^6 + 654853063806 z^7 + 90276776370 z^8 + 3053109675 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-1847296 + 42408432 z - 525649971 z^2 + 5171876325 z^3 + 8835156601425 z^4 + 32147736848217 z^5 + 30815887837191 z^6 + 9001450954287 z^7 + 657485146395 z^8 + 3730189155 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (14778368 - 350004864 z + 4450656969 z^2 - 44406942888 z^3 + 504555212700 z^4 + 40627112186664 z^5 + 132470862070038 z^6 + 117831555753192 z^7 + 32254039533276 z^8 + 2205513645720 z^9 + 11190567465 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (6994922528248179525 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]