Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b76y)

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=-45/8, b>=a

For fixed z and a=-45/8, b=39/8

http://functions.wolfram.com/07.23.03.b76y.01

Input Form

Hypergeometric2F1[-(45/8), 39/8, 19/4, z] == (1/(587189905815 z^4)) (8 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (2148146 + 8104369 z + 41330887 z^2 + 426281440 z^3 - 6724440531 z^4 + 24233251977 z^5 - 40556456512 z^6 + 35871556864 z^7 - 16330096640 z^8 + 3027042304 z^9) + (1/Sqrt[1 - z]) (-8592584 - 28121184 z - 148040737 z^2 - 1617874765 z^3 + 64472721301 z^4 - 338079311919 z^5 + 795925302832 z^6 - 1023972728064 z^7 + 749602979840 z^8 - 294579011584 z^9 + 48432676864 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]