Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b68i)

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=-33/8

http://functions.wolfram.com/07.23.03.b68i.01

Input Form

Hypergeometric2F1[-(45/8), -(33/8), 15/4, z] == (1/(324681477333 z^3)) (4 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (1351980 - 44567055 z + 1287648285 z^2 + 73456152813 z^3 + 345263985585 z^4 + 432341341219 z^5 + 160307775719 z^6 + 13818229439 z^7 - 1843105 z^8 + (1/Sqrt[1 - z]) (-1351980 + 45243045 z - 1309762815 z^2 - 32232630387 z^3 - 75012873939 z^4 + 16425734723 z^5 + 71480766819 z^6 + 19913710159 z^7 + 698536795 z^8 - 7372420 z^9)))

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]