Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.alc5)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=9/4, b>=a

For fixed z and a=9/4, b=19/4

http://functions.wolfram.com/07.23.03.alc5.01

Input Form

Hypergeometric2F1[9/4, 19/4, -(11/2), -z] == (1/(24640 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((1/(1 + z)^12) (2 (6160 + 85120 z + 564655 z^2 + 2443995 z^3 + 8129041 z^4 + 25152545 z^5 - 464220599 z^6 + 208086149 z^7 - 1016025 z^8 - 40641 z^9)) + (1/(1 + z)^(25/2)) (12320 + 176400 z + 1212890 z^2 + 5432135 z^3 + 18571072 z^4 + 57887401 z^5 + 1469525478 z^6 - 1240773959 z^7 + 106479420 z^8 + 4186023 z^9 + 162564 z^10)))

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]