Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9ja)

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=-41/8, b>=a

For fixed z and a=-41/8, b=43/8

http://functions.wolfram.com/07.23.03.b9ja.01

Input Form

Hypergeometric2F1[-(41/8), 43/8, -(9/4), z] == (143640 (1 + Sqrt[1 - z]) + 7980 (172 + 181 Sqrt[1 - z]) z + 399 (35341 + 37196 Sqrt[1 - z]) z^2 + 399 (1309947 + 1329020 Sqrt[1 - z]) z^3 - 16 (327261769 + 263344016 Sqrt[1 - z]) z^4 + 3328 (5027131 + 3025348 Sqrt[1 - z]) z^5 - 1064960 (22845 + 9112 Sqrt[1 - z]) z^6 + 14483456 (1153 + 228 Sqrt[1 - z]) z^7 - 4402970624 z^8)/(143640 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1 - z)^(5/2))

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]