Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c4jg)

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.c4jg.01

Input Form

Hypergeometric2F1[13/8, 33/8, -(23/4), z] == (-699200 + 8550000 z - 49093000 z^2 + 178035035 z^3 - 470594555 z^4 + 1044008250 z^5 - 2758206750 z^6 - 3358137249 z^7 - 34561551 z^8 + 1735308 z^9 + (1/Sqrt[1 - z]) (-699200 + 8899600 z - 53280600 z^2 + 201556485 z^3 - 553982510 z^4 + 1259804595 z^5 - 3230815500 z^6 - 16825878501 z^7 - 2697536286 z^8 + 143018301 z^9 - 6941232 z^10))/ (699200 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + 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]