Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc7r)

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=-37/8, b>=a

For fixed z and a=-37/8, b=39/8

http://functions.wolfram.com/07.23.03.bc7r.01

Input Form

Hypergeometric2F1[-(37/8), 39/8, 9/2, -z] == (256 (Sqrt[z] (-51504 + 232841 z - 1311206 z^2 + 60564677 z^3 + 417061140 z^4 + 1015196160 z^5 + 1177211904 z^6 + 663945216 z^7 + 147062784 z^8) Cos[(3 ArcTan[Sqrt[z]])/4] - (-68672 + 300440 z - 1700705 z^2 + 23685402 z^3 + 237765603 z^4 + 656721120 z^5 + 816321792 z^6 + 481873920 z^7 + 110297088 z^8) Sin[(3 ArcTan[Sqrt[z]])/4]))/(10905809145 z^(7/2) (1 + z)^(3/8))

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]