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

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=-11/8

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

Input Form

Hypergeometric2F1[-(37/8), -(11/8), 11/2, z] == (1/(14740357736195 z^(9/2))) (1024 (-4 Sqrt[z] (-360528 + 5495906 z - 43354565 z^2 + 265374360 z^3 - 5943585313 z^4 - 12397150640 z^5 - 3348452631 z^6 + 135384440 z^7 - 11427251 z^8 + 603198 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((1922816 - 30953904 z + 256196991 z^2 - 1611888498 z^3 + 13707644745 z^4 + 27889309452 z^5 - 27072803079 z^6 - 13659016578 z^7 + 564090663 z^8 - 46915400 z^9 + 2412792 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]