Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a85g)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-21/4

http://functions.wolfram.com/07.23.03.a85g.01

Input Form

Hypergeometric2F1[-(21/4), -(21/4), 11/2, z] == (8 (8 Sqrt[z] (-788970 + 21133125 z - 320276736 z^2 + 4261384764 z^3 + 2033058617772 z^4 + 9590967758190 z^5 + 12488612659600 z^6 + 5392744984284 z^7 + 708957083694 z^8 + 18267208117 z^9) EllipticE[(1/2) (1 - Sqrt[z])] + 8 Sqrt[z] (-788970 + 21133125 z - 320276736 z^2 + 4261384764 z^3 + 2033058617772 z^4 + 9590967758190 z^5 + 12488612659600 z^6 + 5392744984284 z^7 + 708957083694 z^8 + 18267208117 z^9) EllipticE[(1/2) (1 + Sqrt[z])] - (6311760 - 3155880 Sqrt[z] - 173798820 z + 84532500 z^(3/2) + 2688302565 z^2 - 1281106944 z^(5/2) - 35994073752 z^3 + 17045539056 z^(7/2) + 810915673932 z^4 + 8132234471088 z^(9/2) + 14524748369040 z^5 + 38363871032760 z^(11/2) + 44626560168190 z^6 + 49954450638400 z^(13/2) + 44157444460920 z^7 + 21570979937136 z^(15/2) + 15223500754428 z^8 + 2835828334776 z^(17/2) + 1605461431732 z^9 + 73068832468 z^(19/2) + 31121455365 z^10) EllipticK[(1/2) (1 - Sqrt[z])] + (6311760 + 3155880 Sqrt[z] - 173798820 z - 84532500 z^(3/2) + 2688302565 z^2 + 1281106944 z^(5/2) - 35994073752 z^3 - 17045539056 z^(7/2) + 810915673932 z^4 - 8132234471088 z^(9/2) + 14524748369040 z^5 - 38363871032760 z^(11/2) + 44626560168190 z^6 - 49954450638400 z^(13/2) + 44157444460920 z^7 - 21570979937136 z^(15/2) + 15223500754428 z^8 - 2835828334776 z^(17/2) + 1605461431732 z^9 - 73068832468 z^(19/2) + 31121455365 z^10) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)/ (272801524360365 Pi^(3/2) z^(9/2))

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]