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

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=43/8, b>=a

For fixed z and a=43/8, b=47/8

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

Input Form

Hypergeometric2F1[43/8, 47/8, -(9/2), -z] == (1/(64512 (1 + z)^(123/8))) ((64512 + 1426432 z + 16530516 z^2 + 142859787 z^3 + 1205709869 z^4 + 18662626983 z^5 - 123966468951 z^6 + 159485520257 z^7 - 58702391769 z^8 + 5525515917 z^9 - 60896913 z^10) Cos[(3 ArcTan[Sqrt[z]])/4] + Sqrt[z] (48384 + 1062768 z + 12244517 z^2 + 105393939 z^3 + 889305417 z^4 - 63311311297 z^5 + 165519538191 z^6 - 113007527367 z^7 + 21838154947 z^8 - 853728699 z^9) Sin[(3 ArcTan[Sqrt[z]])/4])

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]