Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9tr)

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=-19/8

http://functions.wolfram.com/07.23.03.b9tr.01

Input Form

Hypergeometric2F1[-(39/8), -(19/8), 13/4, z] == (1/(183230845 z^3)) (4 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (14260 - 378603 z + 16763343 z^2 + 108155182 z^3 + 118939890 z^4 + 24177153 z^5 - 297221 z^6 + 12876 z^7 + (1/Sqrt[1 - z]) (-14260 + 385733 z - 16950862 z^2 - 76916089 z^3 + 11647544 z^4 + 72496739 z^5 + 9744986 z^6 - 410959 z^7 + 17168 z^8)))

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]