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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-15/4, b>=a

For fixed z and a=-15/4, b=23/4

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

Input Form

Hypergeometric2F1[-(15/4), 23/4, 9/2, -z] == (8 Sqrt[2] (40 - 256 z + 1733 z^2 - 26055 z^3 - 239544 z^4 - 563472 z^5 - 521664 z^6 - 169728 z^7 + (1/Sqrt[1 + z]) (2 (-20 + 118 z - 800 z^2 + 12577 z^3 + 183483 z^4 + 634848 z^5 + 944112 z^6 + 648960 z^7 + 169728 z^8))))/ (1826565 z^(7/2) Sqrt[-1 + Sqrt[1 + z]])

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]