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

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.anro.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), 1/2}, z] == (1/147349125) (147349125 - 1768189500 z + 5959453500 z^2 - 13621608000 z^3 + 29772943200 z^4 - 83805321600 z^5 + 586637251200 z^6 + 1482709536000 z^7 + 1186167628800 z^8 + 465454503360 z^9 + 103820270400 z^10 + 14077849200 z^11 + 1193139120 z^12 + 63100800 z^13 + 2010112 z^14 + 35072 z^15 + 256 z^16) + (1/147349125) (8 E^z Sqrt[Pi] (129737084400 z^(13/2) + 240940299600 z^(15/2) + 172528517700 z^(17/2) + 63945674100 z^(19/2) + 13791618225 z^(21/2) + 1830653055 z^(23/2) + 152965890 z^(25/2) + 8011080 z^(27/2) + 253440 z^(29/2) + 4400 z^(31/2) + 32 z^(33/2)) 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]