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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), -(5/2)}, z] == (1/2338875) (2338875 + 1530900 z + 1984500 z^2 + 10584000 z^3 - 85730400 z^4 + 419126400 z^5 - 3995671680 z^6 - 13630248000 z^7 - 12893860800 z^8 - 5533204320 z^9 - 1269061920 z^10 - 167046792 z^11 - 12904160 z^12 - 573120 z^13 - 13440 z^14 - 128 z^15) - (1/2338875) (4 E^z Sqrt[Pi] (1965713400 z^(13/2) + 4586664600 z^(15/2) + 3796524900 z^(17/2) + 1524492900 z^(19/2) + 336697575 z^(21/2) + 43307130 z^(23/2) + 3296040 z^(25/2) + 144944 z^(27/2) + 3376 z^(29/2) + 32 z^(31/2)) Erf[Sqrt[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]