Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c5fh)

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=35/8

http://functions.wolfram.com/07.23.03.c5fh.01

Input Form

Hypergeometric2F1[15/8, 35/8, -(17/4), z] == (1209312 (1 + Sqrt[1 - z]) - 35568 (429 + 412 Sqrt[1 - z]) z + 1026 (90767 + 83773 Sqrt[1 - z]) z^2 - 57 (6702925 + 5979778 Sqrt[1 - z]) z^3 + 399 (3384777 + 2982400 Sqrt[1 - z]) z^4 - 7182 (1439383 + 1361798 Sqrt[1 - z]) z^5 - 2 (5900451322 + 3807899771 Sqrt[1 - z]) z^6 - 170765 (5709 + 226 Sqrt[1 - z]) z^7 + 512295 (105 + 4 Sqrt[1 - z]) z^8 - 2732240 z^9)/(1209312 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (1 - z)^(21/2))

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]