Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c4jq)

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=13/8, b>=a

For fixed z and a=13/8, b=33/8

http://functions.wolfram.com/07.23.03.c4jq.01

Input Form

Hypergeometric2F1[13/8, 33/8, -(15/4), z] == (-6800 + 73780 z - 388365 z^2 + 1424600 z^3 - 5541150 z^4 - 9900912 z^5 - 154413 z^6 + 9804 z^7 + (1/Sqrt[1 - z]) (-6800 + 77180 z - 424405 z^2 + 1609985 z^3 - 6209250 z^4 - 44166738 z^5 - 9419193 z^6 + 644613 z^7 - 39216 z^8))/(6800 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + 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]