Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akd9)

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=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.akd9.01

Input Form

HypergeometricPFQ[{3, 9/2}, {-(7/2), 11/2}, -z] == -((1/(35 z^4)) (3 (2822400 + 940800 z + 282240 z^2 + 67200 z^3 + 13055 z^4 + 2130 z^5 + 296 z^6 + 32 z^7 - 10 z^8 + 4 z^9))) + (1/(35 z^(9/2))) ((3 Sqrt[Pi] (1411200 + 1411200 z + 705600 z^2 + 235200 z^3 + 58800 z^4 + 11760 z^5 + 1960 z^6 + 280 z^7 + 35 z^8 - 12 z^9 + 4 z^10) Erfi[Sqrt[z]])/E^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]