Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b759)

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=37/8

http://functions.wolfram.com/07.23.03.b759.01

Input Form

Hypergeometric2F1[-(45/8), 37/8, 11/2, z] == (1/(43546758255 z^(9/2))) (1024 (Sqrt[z] (248640 + 108040 z + 198801 z^2 + 728937 z^3 + 50472991 z^4 - 292197717 z^5 + 682705380 z^6 - 849536240 z^7 + 596920320 z^8 - 224759040 z^9 + 35425280 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((-331520 + 139120 z - 130943 z^2 - 734820 z^3 - 9750462 z^4 + 146431752 z^5 - 556854907 z^6 + 1045522100 z^7 - 1122115600 z^8 + 704871680 z^9 - 242471680 z^10 + 35425280 z^11) 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]