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

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.ahaf.01

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), -(9/2)}, z] == (1/147349125) (147349125 + 53581500 z + 29767500 z^2 + 31752000 z^3 + 85730400 z^4 + 1257379200 z^5 - 59935075200 z^6 - 650041459200 z^7 - 1394164396800 z^8 - 1198245646080 z^9 - 522726946560 z^10 - 129692687040 z^11 - 19417890240 z^12 - 1800923040 z^13 - 103321728 z^14 - 3542272 z^15 - 66048 z^16 - 512 z^17) - (1/147349125) (16 E^z Sqrt[Pi] (11794280400 z^(13/2) + 66834255600 z^(15/2) + 114589528200 z^(17/2) + 88286700600 z^(19/2) + 36231737850 z^(21/2) + 8663458230 z^(23/2) + 1266926535 z^(25/2) + 115680810 z^(27/2) + 6566280 z^(29/2) + 223440 z^(31/2) + 4144 z^(33/2) + 32 z^(35/2)) 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]