Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c5kt)

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=15/8, b>=a

For fixed z and a=15/8, b=43/8

http://functions.wolfram.com/07.23.03.c5kt.01

Input Form

Hypergeometric2F1[15/8, 43/8, -(21/4), z] == (52416 - 739440 z + 5017896 z^2 - 22290579 z^3 + 76693890 z^4 - 253728405 z^5 + 2121684180 z^6 + 1823608435 z^7 + 13164690 z^8 - 1241275 z^9 + 68880 z^10 + (1/Sqrt[1 - z]) (52416 - 765648 z + 5381064 z^2 - 24710373 z^3 + 87256110 z^4 - 289575195 z^5 + 2240177940 z^6 + 2758313525 z^7 + 257579630 z^8 - 18963525 z^9 + 1733480 z^10 - 91840 z^11))/(52416 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]