Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b509)

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=-3/8

http://functions.wolfram.com/07.23.03.b509.01

Input Form

Hypergeometric2F1[-(47/8), -(3/8), 21/4, z] == (1/(1479998648205 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (6970288 - 101739396 z + 756711891 z^2 - 4332101014 z^3 + 49365020589 z^4 + 63839849544 z^5 - 6810153955 z^6 + 2001104226 z^7 - 479189997 z^8 + 75831056 z^9 - 5768448 z^10 + (1/Sqrt[1 - z]) (-6970288 + 105224540 z - 806710303 z^2 + 4698175178 z^3 - 51442568545 z^4 + 6594616772 z^5 + 49612222671 z^6 - 11339590614 z^7 + 3210640257 z^8 - 725026100 z^9 + 107677696 z^10 - 7691264 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]