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

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=6, b₁>=-11/2

For fixed z and a₁=4, a₂=6, b₁=1

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

Input Form

HypergeometricPFQ[{4, 6}, {1, 9/2}, -z] == (7 (675 + 90 z + 180 z^2 + 11736 z^3 - 30192 z^4 + 15840 z^5 - 2624 z^6 + 128 z^7))/(98304 z^3) - (1/(196608 z^(7/2))) ((7 Sqrt[Pi] (675 + 540 z + 360 z^2 - 2160 z^3 + 43200 z^4 - 73920 z^5 + 34176 z^6 - 5376 z^7 + 256 z^8) 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]