Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bcd2)

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=47/8

http://functions.wolfram.com/07.23.03.bcd2.01

Input Form

Hypergeometric2F1[-(37/8), 47/8, 15/4, z] == (1/(1546593255 z^3)) (4 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (30044 + 393791 z + 6911193 z^2 - 158554660 z^3 + 686844928 z^4 - 1202488320 z^5 + 940769280 z^6 - 273940480 z^7 - (1/Sqrt[1 - z]) (30044 + 378769 z + 6710542 z^2 - 355385515 z^3 + 2250606512 z^4 - 5788870912 z^5 + 7307182080 z^6 - 4516413440 z^7 + 1095761920 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]