Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.am6w)

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=3, b>=a

For fixed z and a=3, b=6

http://functions.wolfram.com/07.23.03.am6w.01

Input Form

Hypergeometric2F1[3, 6, -(21/4), z] == (1/3244294144) ((1/(-1 + z)^14) (8 (405536768 - 7067926528 z + 60949790720 z^2 - 357055856640 z^3 + 1704658206720 z^4 - 8421927026688 z^5 + 117443211296768 z^6 + 243583966264625 z^7 + 82063914858980 z^8 + 1439420382400 z^9 - 70431320960 z^10 + 2526684160 z^11)) - (1/(1 - z)^(57/4)) (336882996450 Sqrt[2] z^(25/4) (957 + 1320 z + 320 z^2) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(57/4)) (336882996450 Sqrt[2] z^(25/4) (957 + 1320 z + 320 z^2) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (168441498225 Sqrt[2] z^(25/4) (957 + 1320 z + 320 z^2) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(57/4) - (168441498225 Sqrt[2] z^(25/4) (957 + 1320 z + 320 z^2) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(57/4))

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]