Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am9q)

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=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.am9q.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(11/2), -(11/2)}, z] == (1/306338830875) (306338830875 + 222791877000 z + 178783605000 z^2 + 218918700000 z^3 + 521026506000 z^4 + 3519823507200 z^5 + 221748880953600 z^6 + 11403454575744000 z^7 + 59137895629612800 z^8 + 103945471093094400 z^9 + 86998410287585280 z^10 + 40647187118039040 z^11 + 11582527180492800 z^12 + 2121551788769280 z^13 + 257486839480320 z^14 + 20994094301184 z^15 + 1148262776832 z^16 + 41316761600 z^17 + 933052416 z^18 + 11927552 z^19 + 65536 z^20) + (1/306338830875) (8192 E^z Sqrt[Pi] (193396896000 z^(13/2) + 3055670956800 z^(15/2) + 11133973065600 z^(17/2) + 16547010480000 z^(19/2) + 12614576990400 z^(21/2) + 5569241832000 z^(23/2) + 1530309322080 z^(25/2) + 273567080160 z^(27/2) + 32648601150 z^(29/2) + 2630454090 z^(31/2) + 142635405 z^(33/2) + 5099781 z^(35/2) + 114622 z^(37/2) + 1460 z^(39/2) + 8 z^(41/2)) 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]