Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9539)

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=-23/4, b>=a

For fixed z and a=-23/4, b=3/4

http://functions.wolfram.com/07.23.03.9539.01

Input Form

Hypergeometric2F1[-(23/4), 3/4, 9/2, -z] == (8 Sqrt[2] (-2 (8740 + 90022 z + 438748 z^2 + 1601605 z^3 + 779592 z^4 + 649660 z^5 + 385344 z^6 + 151361 z^7 + 35280 z^8 + 3696 z^9) + (1/Sqrt[1 + z]) (17480 + 188784 z + 965333 z^2 + 3620545 z^3 + 5507106 z^4 + 4987378 z^5 + 3720953 z^6 + 1987101 z^7 + 710360 z^8 + 152208 z^9 + 14784 z^10)))/(39126945 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]