Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7eh)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-39/8

http://functions.wolfram.com/07.23.03.b7eh.01

Input Form

Hypergeometric2F1[-(43/8), -(39/8), 13/4, z] == (4 2^(1/4) (2 (459885 - 19959009 z + 6910048085 z^2 + 63197672863 z^3 + 140257912543 z^4 + 96863765653 z^5 + 19939083615 z^6 + 845589165 z^7) + (1/Sqrt[1 - z]) (-919770 + 40377903 z + 7316678431 z^2 + 39184409883 z^3 + 26230163159 z^4 - 39413665171 z^5 - 29474914355 z^6 - 3829949175 z^7 - 52180905 z^8)))/(84626474555 (1 + Sqrt[1 - z])^(1/4) z^2)

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]