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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=6, b>=a

For fixed z and a=6, b=6

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

Input Form

Hypergeometric2F1[6, 6, -(19/4), z] == (1/561030103040) (-((1/(-1 + z)^16) (8 (-70128762880 + 1653562408960 z - 20391967850496 z^2 + 185550103379968 z^3 - 1584693413675008 z^4 + 19750502673678336 z^5 + 218016558838076005 z^6 + 386675327425980704 z^7 + 202296537367476048 z^8 + 30961470740433152 z^9 + 933425756586496 z^10))) + (1/(1 - z)^(67/4)) (157437950670 Sqrt[2] z^(23/4) (3275181 + 12130300 z + 12521600 z^2 + 4293120 z^3 + 440320 z^4 + 8192 z^5) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(67/4)) (157437950670 Sqrt[2] z^(23/4) (3275181 + 12130300 z + 12521600 z^2 + 4293120 z^3 + 440320 z^4 + 8192 z^5) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(67/4)) (78718975335 Sqrt[2] z^(23/4) (3275181 + 12130300 z + 12521600 z^2 + 4293120 z^3 + 440320 z^4 + 8192 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(67/4)) (78718975335 Sqrt[2] z^(23/4) (3275181 + 12130300 z + 12521600 z^2 + 4293120 z^3 + 440320 z^4 + 8192 z^5) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

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]