Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb6w)

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=-35/8

http://functions.wolfram.com/07.23.03.bb6w.01

Input Form

Hypergeometric2F1[-(37/8), -(35/8), 11/2, z] == (1/(605906283787805 z^(9/2))) (1024 (Sqrt[z] (4326336 - 99789000 z + 1273858089 z^2 - 13854077055 z^3 + 841617991901 z^4 + 4535689894837 z^5 + 6032216577435 z^6 + 2483942398787 z^7 + 283627838431 z^8 + 4946525199 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-5768448 + 137979216 z - 1811933253 z^2 + 19918541076 z^3 - 348940630080 z^4 - 2639168954220 z^5 - 1861376666978 z^6 + 2597984937948 z^7 + 1959581827416 z^8 + 268734142124 z^9 + 4946525199 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]