Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7hl)

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=19/8, b>=a

For fixed z and a=19/8, b=39/8

http://functions.wolfram.com/07.23.03.c7hl.01

Input Form

Hypergeometric2F1[19/8, 39/8, -(9/4), z] == (1/(85560 2^(1/4) (-1 + z)^9)) ((1 + Sqrt[1 - z])^(1/4) (-42780 + 602485 z - 5230568 z^2 - 120647906 z^3 - 90998488 z^4 - 990379 z^5 + 55796 z^6 + (1/Sqrt[1 - z]) (-42780 + 623875 z - 5526463 z^2 + 317067998 z^3 + 488311446 z^4 + 72465055 z^5 - 4114955 z^6 + 223184 z^7)))

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]