Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b64x)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-43/8

http://functions.wolfram.com/07.23.03.b64x.01

Input Form

Hypergeometric2F1[-(45/8), -(43/8), 9/2, z] == (1/(605906283787805 z^(7/2))) (256 (Sqrt[z] (-33220080 + 1073700669 z - 22874239752 z^2 + 3114696337484 z^3 + 28775809762472 z^4 + 70517867161550 z^5 + 60321373299656 z^6 + 18251801425292 z^7 + 1644030509576 z^8 + 23633398173 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((44293440 - 1469434872 z + 31720331805 z^2 - 1023170712648 z^3 - 15426661091412 z^4 - 34617979117928 z^5 + 775384050542 z^6 + 33592121724360 z^7 + 15076264916588 z^8 + 1570111641952 z^9 + 23633398173 z^10) Sin[(3 ArcSin[Sqrt[z]])/4])))

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]