Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bjf4)

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=-25/8, b>=a

For fixed z and a=-25/8, b=35/8

http://functions.wolfram.com/07.23.03.bjf4.01

Input Form

Hypergeometric2F1[-(25/8), 35/8, 23/4, z] == (16 2^(3/4) (3400 - 2040 z - 2295 z^2 - 4250 z^3 + 350433 z^4 - 764064 z^5 + 593152 z^6 - 159744 z^7 + (1/Sqrt[1 - z]) (4 (-850 + 935 z + 425 z^2 + 765 z^3 + 95577 z^4 - 328692 z^5 + 421792 z^6 - 243200 z^7 + 53248 z^8))))/ (11762361 (1 + Sqrt[1 - z])^(3/4) z^4)

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]