Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bg98)

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=-29/8, b>=a

For fixed z and a=-29/8, b=-25/8

http://functions.wolfram.com/07.23.03.bg98.01

Input Form

Hypergeometric2F1[-(29/8), -(25/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (80773120 - 1408796800 z + 12705682275 z^2 - 85704672950 z^3 + 618196918625 z^4 + 24515510454876 z^5 + 38786442531445 z^6 + 13084060402490 z^7 + 784718654055 z^8) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (80773120 - 1408796800 z + 12705682275 z^2 - 85704672950 z^3 + 618196918625 z^4 + 24515510454876 z^5 + 38786442531445 z^6 + 13084060402490 z^7 + 784718654055 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (80773120 - 1408796800 z + 12705682275 z^2 - 85704672950 z^3 + 618196918625 z^4 + 24515510454876 z^5 + 38786442531445 z^6 + 13084060402490 z^7 + 784718654055 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-80773120 + 1439086720 z - 13225698675 z^2 + 90329247125 z^3 - 649107205175 z^4 - 5227761306351 z^5 + 203975060471 z^6 + 4557111468175 z^7 + 1017818147955 z^8 + 19501972875 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (4997531405238597225 Pi (1 + Sqrt[1 - z])^(1/4) (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]