Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c7h6)

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.c7h6.01

Input Form

Hypergeometric2F1[19/8, 39/8, -(21/4), z] == (1/(5430208 2^(1/4) (-1 + z)^12)) ((1 + Sqrt[1 - z])^(1/4) (2 (1357552 - 19199664 z + 131338165 z^2 - 593797808 z^3 + 2116944771 z^4 - 7527852574 z^5 - 72020331237 z^6 - 30976673220 z^7 - 176919459 z^8 + 6938018 z^9) + (1/Sqrt[1 - z]) (2715104 - 39756880 z + 281536606 z^2 - 1314303559 z^3 + 4797146708 z^4 - 17039192005 z^5 + 445592185230 z^6 + 403451896143 z^7 + 38131346928 z^8 - 1453514771 z^9 + 55504144 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]