Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4me)

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=-43/8

http://functions.wolfram.com/07.23.03.b4me.01

Input Form

Hypergeometric2F1[-(47/8), -(43/8), 17/4, z] == (1/(6177732642515 z^4)) (8 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (4 (-1127718 + 39658083 z - 984873720 z^2 + 61704969900 z^3 + 743339945308 z^4 + 2145980498602 z^5 + 2136698881288 z^6 + 774532439068 z^7 + 91570305850 z^8 + 2359894699 z^9) + (1/Sqrt[1 - z]) (4510872 - 160887768 z + 4018247187 z^2 - 248770079928 z^3 - 2464324249820 z^4 - 4318447228216 z^5 + 1012407272082 z^6 + 4282186932152 z^7 + 1595174467372 z^8 + 136568509584 z^9 + 1342506483 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]