Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c8uv)

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=23/8, b>=a

For fixed z and a=23/8, b=35/8

http://functions.wolfram.com/07.23.03.c8uv.01

Input Form

Hypergeometric2F1[23/8, 35/8, -(21/4), z] == (29376 - 428400 z + 3033576 z^2 - 14259699 z^3 + 53078610 z^4 - 197307957 z^5 + 1989359460 z^6 + 2615928403 z^7 + 470119298 z^8 + 365925 z^9 + (1/Sqrt[1 - z]) (29376 - 443088 z + 3244104 z^2 - 15724773 z^3 + 59854890 z^4 - 222238467 z^5 + 2082162456 z^6 + 3610953797 z^7 + 1010705586 z^8 + 31835475 z^9 - 487900 z^10))/ (29376 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^12)

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]