Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9s3)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-25/8

http://functions.wolfram.com/07.23.03.b9s3.01

Input Form

Hypergeometric2F1[-(39/8), -(25/8), 11/2, z] == (1/(369715992868497 z^(9/2))) (1024 (-2 Sqrt[z] (-159712 + 3237020 z - 35699197 z^2 + 328263061 z^3 - 185395079325 z^4 - 533481015675 z^5 - 354497499807 z^6 - 55370707113 z^7 - 634828647 z^8 + 10407027 z^9) Cos[ArcSin[Sqrt[z]]/4] - (1/Sqrt[1 - z]) ((1277696 - 26774576 z + 303292375 z^2 - 2820376311 z^3 + 40740549773 z^4 + 195859743117 z^5 + 4897240215 z^6 - 184578476133 z^7 - 53117225889 z^8 - 1280064321 z^9 + 20814054 z^10) Sin[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]