Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b505)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-3/8

http://functions.wolfram.com/07.23.03.b505.01

Input Form

Hypergeometric2F1[-(47/8), -(3/8), 17/4, z] == (1/(75555486545 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-2412792 + 35923792 z - 309138975 z^2 + 4726558995 z^3 + 7461408802 z^4 - 999155850 z^5 + 341787765 z^6 - 93410537 z^7 + 16613520 z^8 - 1403136 z^9 - (1/Sqrt[1 - z]) (4 (-603198 + 9282547 z - 81699818 z^2 + 1219197202 z^3 + 103100695 z^4 - 1568729393 z^5 + 429418660 z^6 - 140348516 z^7 + 35851453 z^8 - 5937344 z^9 + 467712 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]