Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b53q)

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=5/8

http://functions.wolfram.com/07.23.03.b53q.01

Input Form

Hypergeometric2F1[-(47/8), 5/8, 21/4, z] == (1/(119999890395 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (6970288 - 80024268 z + 433397763 z^2 - 1549850239 z^3 + 6825989634 z^4 - 3312829674 z^5 + 2182248695 z^6 - 1074985659 z^7 + 361504836 z^8 - 73690624 z^9 + 6859776 z^10 + (1/Sqrt[1 - z]) (-6970288 + 83509412 z - 472538611 z^2 + 1756981730 z^3 - 7551469273 z^4 + 10306241792 z^5 - 6862035477 z^6 + 4119481146 z^7 - 1841906319 z^8 + 565626208 z^9 - 106066688 z^10 + 9146368 z^11)))

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]