Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bz8l)

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=3/8, b>=a

For fixed z and a=3/8, b=39/8

http://functions.wolfram.com/07.23.03.bz8l.01

Input Form

Hypergeometric2F1[3/8, 39/8, -(21/4), z] == (1/(5430208 2^(1/4) (-1 + z)^10)) ((1 + Sqrt[1 - z])^(1/4) (2 (1357552 - 13963392 z + 65422741 z^2 - 185618855 z^3 + 361426830 z^4 - 545899894 z^5 - 199413831 z^6 + 62471133 z^7 - 12682860 z^8 + 1201760 z^9) + (1/Sqrt[1 - z]) (2715104 - 29284336 z + 144469486 z^2 - 433339297 z^3 + 893756195 z^4 - 1413983098 z^5 + 6021937812 z^6 - 1930958997 z^7 + 568736139 z^8 - 108072560 z^9 + 9614080 z^10)))

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]