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

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.anrr.01

Input Form

Hypergeometric2F1[6, 6, -(23/4), z] == (1/12903692369920) (-((1/(-1 + z)^17) (8 (1612961546240 - 37518888140800 z + 443125197701120 z^2 - 3652016597368832 z^3 + 25009111649222656 z^4 - 171764740391960576 z^5 + 1799119130331185152 z^6 + 16623304630434842335 z^7 + 25620200675994881968 z^8 + 11866758682227008816 z^9 + 1629564784843568384 z^10 + 44515876405509632 z^11))) - (1/(1 - z)^(71/4)) (7399583681490 Sqrt[2] z^(27/4) (5701241 + 18391100 z + 16814720 z^2 + 5173760 z^3 + 481280 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)^(71/4)) (7399583681490 Sqrt[2] z^(27/4) (5701241 + 18391100 z + 16814720 z^2 + 5173760 z^3 + 481280 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)^(71/4)) (3699791840745 Sqrt[2] z^(27/4) (5701241 + 18391100 z + 16814720 z^2 + 5173760 z^3 + 481280 z^4 + 8192 z^5) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) + (1/(1 - z)^(71/4)) (3699791840745 Sqrt[2] z^(27/4) (5701241 + 18391100 z + 16814720 z^2 + 5173760 z^3 + 481280 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]