Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4re)

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=-27/8

http://functions.wolfram.com/07.23.03.b4re.01

Input Form

Hypergeometric2F1[-(47/8), -(27/8), 17/4, z] == (1/(3544600696525 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (-1809594 + 48959571 z - 897860223 z^2 + 39217521168 z^3 + 309450960623 z^4 + 522550474908 z^5 + 250049892663 z^6 + 27722553836 z^7 - 164294541 z^8 + 4606389 z^9) + (1/Sqrt[1 - z]) (7238376 - 199457472 z + 3688455237 z^2 - 158641777731 z^3 - 938268229591 z^4 - 487568335471 z^5 + 997011055679 z^6 + 549381164151 z^7 + 35462541627 z^8 - 897222213 z^9 + 24567408 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]