Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5ms)

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=-47/8, b>=a

For fixed z and a=-47/8, b=37/8

http://functions.wolfram.com/07.23.03.b5ms.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 21/4, z] == (1/(119999890395 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (6970288 + 6836244 z + 20810331 z^2 + 111960251 z^3 + 2786071029 z^4 - 18735094539 z^5 + 46930228796 z^6 - 61212856320 z^7 + 44592159744 z^8 - 17292132352 z^9 + 2794192896 z^10 + (1/Sqrt[1 - z]) (-6970288 - 3351100 z - 16520923 z^2 - 100264912 z^3 - 2726790070 z^4 + 23893879940 z^5 - 76521715239 z^6 + 130667150064 z^7 - 131698076928 z^8 + 79025520640 z^9 - 26238451712 z^10 + 3725590528 z^11)))

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]