Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bfm1)

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=-31/8, b>=a

For fixed z and a=-31/8, b=37/8

http://functions.wolfram.com/07.23.03.bfm1.01

Input Form

Hypergeometric2F1[-(31/8), 37/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (2 (28995824 - 78162656 z + 33404085 z^2 + 25433551 z^3 + 23839595 z^4 + 27645033 z^5 - 669844392 z^6 + 1116836160 z^7 - 702434304 z^8 + 158146560 z^9) + (1/Sqrt[1 - z]) (57991648 - 185321136 z + 137721870 z^2 + 33379203 z^3 + 21399651 z^4 + 25437321 z^5 + 1528319603 z^6 - 4275021600 z^7 + 4564124928 z^8 - 2233380864 z^9 + 421724160 z^10)))/ (115983296 2^(3/4) (-1 + z)^6)

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]