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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), 3/2}, -z] == (1/147349125) (147349125 + 589396500 z + 1191890700 z^2 + 1945944000 z^3 + 3308104800 z^4 + 7618665600 z^5 + 45125942400 z^6 - 88962572160 z^7 + 56691835200 z^8 - 17726718240 z^9 + 3120400800 z^10 - 327333000 z^11 + 20738784 z^12 - 772800 z^13 + 15488 z^14 - 128 z^15) + (1/147349125) ((4 Sqrt[Pi] z^(13/2) (-18533869200 + 27800803800 z - 16080857100 z^2 + 4786481700 z^3 - 818648775 z^4 + 84333690 z^5 - 5279400 z^6 + 195120 z^7 - 3888 z^8 + 32 z^9) 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]