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

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=-11/2

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

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), -(7/2)}, -z] == (1/343814625) (343814625 - 321489000 z + 392931000 z^2 - 972972000 z^3 + 10216206000 z^4 + 185253868800 z^5 + 3519823507200 z^6 - 24234389222400 z^7 + 40799712441600 z^8 - 29920449484800 z^9 + 11652318996480 z^10 - 2654619770880 z^11 + 371991244800 z^12 - 32735969280 z^13 + 1800437760 z^14 - 59643904 z^15 + 1081344 z^16 - 8192 z^17) + (1/343814625) ((1024 Sqrt[Pi] (-8790768000 z^(13/2) + 36335174400 z^(15/2) - 50848560000 z^(17/2) + 33951052800 z^(19/2) - 12526768800 z^(21/2) + 2760004800 z^(23/2) - 378446040 z^(25/2) + 32820000 z^(27/2) - 1786845 z^(29/2) + 58770 z^(31/2) - 1060 z^(33/2) + 8 z^(35/2)) 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]