Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7b0)

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=47/8

http://functions.wolfram.com/07.23.03.b7b0.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, -(21/4), z] == (1/(70592704 2^(1/4) (-1 + z)^5)) ((1 + Sqrt[1 - z])^(1/4) (-35296352 - 47902192 z - 76951238 z^2 - 152876469 z^3 - 409846660 z^4 - 1806611521 z^5 + 53072188048 z^6 - 162401065728 z^7 + 203397021696 z^8 - 117588951040 z^9 + 26079133696 z^10 + (1/Sqrt[1 - z]) (2 (-17648176 - 15127008 z - 24294049 z^2 - 53103527 z^3 - 159708435 z^4 - 787466433 z^5 - 61184617076 z^6 + 304106479776 z^7 - 587243999232 z^8 + 564200243200 z^9 - 271036710912 z^10 + 52158267392 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]