Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc2f)

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=-37/8, b>=a

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

http://functions.wolfram.com/07.23.03.bc2f.01

Input Form

Hypergeometric2F1[-(37/8), 31/8, 15/4, z] == (1/(2544395355 z^3)) (4 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (390572 + 1827319 z + 16599310 z^2 - 216600065 z^3 + 624796368 z^4 - 784806528 z^5 + 463017984 z^6 - 105431040 z^7 - (1/Sqrt[1 - z]) (390572 + 1632033 z + 15636829 z^2 - 543201965 z^3 + 2390049827 z^4 - 4522155168 z^5 + 4377931008 z^6 - 2142007296 z^7 + 421724160 z^8)))

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]