Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akoz)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=3, a₂>=3

For fixed z and a₁=3, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.akoz.01

Input Form

HypergeometricPFQ[{3, 11/2}, {-(3/2), -(1/2)}, z] == (1/2835) (2835 + 62370 z - 3243240 z^2 - 33732720 z^3 - 62823600 z^4 - 43140384 z^5 - 13778688 z^6 - 2250624 z^7 - 191616 z^8 - 8000 z^9 - 128 z^10) - (1/2835) (32 E^z Sqrt[Pi] (317520 z^(5/2) + 1678320 z^(7/2) + 2487240 z^(9/2) + 1534680 z^(11/2) + 463050 z^(13/2) + 73206 z^(15/2) + 6111 z^(17/2) + 252 z^(19/2) + 4 z^(21/2)) Erf[Sqrt[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},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]