Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9fp)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-41/8, b>=a

For fixed z and a=-41/8, b=35/8

http://functions.wolfram.com/07.23.03.b9fp.01

Input Form

Hypergeometric2F1[-(41/8), 35/8, 11/2, -z] == -((1024 (4 Sqrt[z] (-1951600 - 731850 z + 1000195 z^2 - 3185290 z^3 - 128242952 z^4 - 274992004 z^5 - 4492355 z^6 + 570777536 z^7 + 722245888 z^8 + 372736000 z^9 + 72417280 z^10) Cos[(7 ArcTan[Sqrt[z]])/4] - (-4460800 + 1394000 z + 3244535 z^2 - 8879780 z^3 + 74892650 z^4 + 1675901164 z^5 + 5695837847 z^6 + 8732202208 z^7 + 7067330816 z^8 + 2957660160 z^9 + 506920960 z^10) Sin[(7 ArcTan[Sqrt[z]])/4]))/(650345524257 z^(9/2) (1 + z)^(7/8)))

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]