Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akm4)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.akm4.01

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(5/2)}, -z] == (1/147349125) (147349125 - 176818950 z + 340540200 z^2 - 2432430000 z^3 - 24810786000 z^4 - 146659312800 z^5 - 1642584303360 z^6 + 6929444712960 z^7 - 8036489260800 z^8 + 4253763064320 z^9 - 1220395714560 z^10 + 205667069952 z^11 - 21104627712 z^12 + 1323786240 z^13 - 49184768 z^14 + 987136 z^15 - 8192 z^16) + (1/147349125) ((2048 Sqrt[Pi] (1696464000 z^(13/2) - 4750099200 z^(15/2) + 4754090880 z^(17/2) - 2335132800 z^(19/2) + 641662560 z^(21/2) - 105280560 z^(23/2) + 10616760 z^(25/2) - 658152 z^(27/2) + 24255 z^(29/2) - 484 z^(31/2) + 4 z^(33/2)) 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]