Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c2ug)

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=9/8, b>=a

For fixed z and a=9/8, b=47/8

http://functions.wolfram.com/07.23.03.c2ug.01

Input Form

Hypergeometric2F1[9/8, 47/8, -(11/2), -z] == (1/(32124928 (1 + z)^(25/2))) ((-Sqrt[1 + z]) (-32124928 - 425107712 z - 2659090720 z^2 - 10592770773 z^3 - 31134589538 z^4 - 78981510491 z^5 - 285350169208 z^6 + 134774127445 z^7 + 25630062134 z^8 + 5101774859 z^9 + 718141732 z^10 + 50044720 z^11) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-8031232 - 108786688 z - 696917572 z^2 - 2842440809 z^3 - 8530724150 z^4 - 21872272487 z^5 - 1262943614572 z^6 + 146994365641 z^7 + 28094309642 z^8 + 5454590135 z^9 + 743164092 z^10 + 50044720 z^11) Sinh[ArcSinh[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]