Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6x3)

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=23/8

http://functions.wolfram.com/07.23.03.b6x3.01

Input Form

Hypergeometric2F1[-(45/8), 23/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-457080832 + 2544297600 z - 4470863735 z^2 + 554891220 z^3 + 1344544110 z^4 - 9147941740 z^5 + 16894693585 z^6 - 16348123440 z^7 + 9086943360 z^8 - 2763171840 z^9 + 358465536 z^10) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-457080832 + 2544297600 z - 4470863735 z^2 + 554891220 z^3 + 1344544110 z^4 - 9147941740 z^5 + 16894693585 z^6 - 16348123440 z^7 + 9086943360 z^8 - 2763171840 z^9 + 358465536 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-457080832 + 2544297600 z - 4470863735 z^2 + 554891220 z^3 + 1344544110 z^4 - 9147941740 z^5 + 16894693585 z^6 - 16348123440 z^7 + 9086943360 z^8 - 2763171840 z^9 + 358465536 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-457080832 + 2715702912 z - 5378106695 z^2 + 1995474195 z^3 + 1472595930 z^4 + 18191121830 z^5 - 63596789795 z^6 + 95580742455 z^7 - 81709156320 z^8 + 41491380480 z^9 - 11739746304 z^10 + 1433862144 z^11) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (7270691817634245 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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</semantics> </math>

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]