Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7pj)

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=-43/8, b>=a

For fixed z and a=-43/8, b=1/8

http://functions.wolfram.com/07.23.03.b7pj.01

Input Form

Hypergeometric2F1[-(43/8), 1/8, 21/4, z] == (16 2^(1/4) (764712 - 9294192 z + 55390149 z^2 - 238499457 z^3 + 4667947242 z^4 - 103461490 z^5 + 39897385 z^6 - 11798765 z^7 + 2220880 z^8 - 195840 z^9 + (1/Sqrt[1 - z]) (4 (-191178 + 2419137 z - 14985414 z^2 + 66270138 z^3 + 244703697 z^4 - 391537795 z^5 + 130006140 z^6 - 47834600 z^7 + 13309555 z^8 - 2355520 z^9 + 195840 z^10))))/(92154224085 (1 + Sqrt[1 - z])^(1/4) 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]