Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am1e)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.am1e.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(5/2), 3/2}, -z] == (1/4725) (4725 + 22680 z + 83160 z^2 + 617760 z^3 - 1441440 z^4 + 895440 z^5 - 232008 z^6 + 28152 z^7 - 1568 z^8 + 32 z^9) - (1/4725) ((4 Sqrt[Pi] z^(7/2) (270270 - 450450 z + 249795 z^2 - 61335 z^3 + 7230 z^4 - 396 z^5 + 8 z^6) 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]