Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9047)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-19/4

http://functions.wolfram.com/07.23.03.9047.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), 6, -z] == (16384 Sqrt[2] ((-Sqrt[1 + z]) (428032 + 10975008 z + 153349779 z^2 + 1717363032 z^3 + 22622819604 z^4 - 631321721688 z^5 + 1813798465458 z^6 - 1509114552216 z^7 + 393671660052 z^8 - 25427340296 z^9 + 79594515 z^10) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - (428032 + 11403040 z + 164324787 z^2 + 1870712811 z^3 + 24340182636 z^4 - 608698902084 z^5 + 1182476743770 z^6 + 304683913242 z^7 - 1115442892164 z^8 + 368244319756 z^9 - 25347745781 z^10 + 79594515 z^11) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (428032 + 10975008 z + 153349779 z^2 + 1717363032 z^3 + 22622819604 z^4 - 631321721688 z^5 + 1813798465458 z^6 - 1509114552216 z^7 + 393671660052 z^8 - 25427340296 z^9 + 79594515 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-428032 - 11296032 z - 161550939 z^2 - 1831617480 z^3 - 23900404836 z^4 - 117437113752 z^5 + 1947191772078 z^6 - 3912080009784 z^7 + 2366646071100 z^8 - 448127845576 z^9 + 19659845205 z^10) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (5995788194340945 Pi z^5 Sqrt[1 + 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]