Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9010)

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=-21/4

http://functions.wolfram.com/07.23.03.9010.01

Input Form

Hypergeometric2F1[-(23/4), -(21/4), 6, z] == (16384 Sqrt[1 + Sqrt[z]] ((15214592 - 416261728 z + 6222790415 z^2 - 74655328504 z^3 + 1051083595940 z^4 + 59607990767736 z^5 + 235366529217306 z^6 + 277898908985400 z^7 + 114288480869028 z^8 + 15108451884840 z^9 + 434830041615 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-15214592 + 15214592 Sqrt[z] + 404850784 z - 404850784 z^(3/2) - 5920935287 z^2 + 5920935287 z^(5/2) + 70261401880 z^3 - 70261401880 z^(7/2) - 999063954980 z^4 + 999063954980 z^(9/2) - 24416429082456 z^5 + 24416429082456 z^(11/2) - 70759875780138 z^6 + 70759875780138 z^(13/2) - 61217774907096 z^7 + 61217774907096 z^(15/2) - 17255147832420 z^8 + 17255147832420 z^(17/2) - 1325902862280 z^9 + 1325902862280 z^(19/2) - 12396127575 z^10 + 12396127575 z^(21/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(294362129962575675 Pi z^5)

Standard Form

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MathML Form

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type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </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]