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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 3}, {-(11/2), 9/2}, -z] == (1/(297 z^3)) (21772800 + 6773760 z + 2016000 z^2 + 470313 z^3 + 89370 z^4 + 14280 z^5 + 1968 z^6 + 240 z^7 + 28 z^8 + 8 z^9) - (1/(297 z^(7/2))) ((2 Sqrt[Pi] (5443200 + 5322240 z + 2600640 z^2 + 846720 z^3 + 206640 z^4 + 40320 z^5 + 6552 z^6 + 912 z^7 + 111 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]