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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{1/2, 6}, {-(5/2), -(1/2)}, z] == (1/1800) (1800 + 4320 z - 30240 z^2 + 268800 z^3 + 708885 z^4 + 459885 z^5 + 120596 z^6 + 14568 z^7 + 800 z^8 + 16 z^9) + (1/3600) (E^z Sqrt[Pi] (984555 z^(7/2) + 1786785 z^(9/2) + 1027650 z^(11/2) + 255000 z^(13/2) + 29920 z^(15/2) + 1616 z^(17/2) + 32 z^(19/2)) 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]