Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6hi)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-7/8

http://functions.wolfram.com/07.23.03.b6hi.01

Input Form

Hypergeometric2F1[-(45/8), -(7/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-3296256 + 49752864 z - 403949091 z^2 + 2932512219 z^3 + 24293534950 z^4 + 7761813542 z^5 - 1323178983 z^6 + 257164127 z^7 - 36673868 z^8 + 2635248 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-3296256 + 49752864 z - 403949091 z^2 + 2932512219 z^3 + 24293534950 z^4 + 7761813542 z^5 - 1323178983 z^6 + 257164127 z^7 - 36673868 z^8 + 2635248 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 (-824064 + 12953256 z - 108676659 z^2 + 795009306 z^3 - 13925611415 z^4 - 20254739642 z^5 - 58130177 z^6 + 11155598 z^7 - 1560757 z^8 + 109802 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-3296256 + 49752864 z - 403949091 z^2 + 2932512219 z^3 + 24293534950 z^4 + 7761813542 z^5 - 1323178983 z^6 + 257164127 z^7 - 36673868 z^8 + 2635248 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2562532509131595 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]