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

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=9/4, b>=a

For fixed z and a=9/4, b=23/4

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

Input Form

Hypergeometric2F1[9/4, 23/4, -(5/2), -z] == (1/(40 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]])) (Sqrt[z] ((20 + 301 z + 2655 z^2 - 167354 z^3 + 167354 z^4 - 2655 z^5 - 301 z^6 - 20 z^7)/(1 + z)^10 + (20 + 311 z + 2803 z^2 + 230494 z^3 - 390302 z^4 + 65795 z^5 + 5759 z^6 + 632 z^7 + 40 z^8)/(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]