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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(9/2), -(9/2)}, -z] == (1/200930625) (200930625 - 208372500 z + 267907500 z^2 - 628689600 z^3 + 4086482400 z^4 - 245188944000 z^5 + 11870281987200 z^6 - 57412701158400 z^7 + 93325371713280 z^8 - 71567211985920 z^9 + 30305803852800 z^10 - 7724881059840 z^11 + 1245151918080 z^12 - 130196656128 z^13 + 8887004352 z^14 - 390458880 z^15 + 10575872 z^16 - 159744 z^17 + 1024 z^18) - (1/200930625) ((32 Sqrt[Pi] (-53330659200 z^(11/2) + 795857529600 z^(13/2) - 2715761260800 z^(15/2) + 3745855411200 z^(17/2) - 2623948236000 z^(19/2) + 1052334642240 z^(21/2) - 259121106720 z^(23/2) + 40820290560 z^(25/2) - 4201794765 z^(27/2) + 283660650 z^(29/2) - 12364632 z^(31/2) + 332976 z^(33/2) - 5008 z^(35/2) + 32 z^(37/2)) 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]