Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6b1)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-25/8

http://functions.wolfram.com/07.23.03.b6b1.01

Input Form

Hypergeometric2F1[-(45/8), -(25/8), 11/4, z] == (1/(1134168387 z^2)) (2 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (2 (-80475 + 3862800 z + 261244107 z^2 + 1230961962 z^3 + 1286525083 z^4 + 285808844 z^5 - 196075 z^6 + 7130 z^7) + (1/Sqrt[1 - z]) (160950 - 7806075 z - 235103436 z^2 - 511359873 z^3 + 268681606 z^4 + 439634403 z^5 + 47343200 z^6 - 1607815 z^7 + 57040 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]