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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(9/2), -(9/2)}, -z] == (1/281302875) (281302875 - 312558750 z + 420997500 z^2 - 1021620600 z^3 + 6810804000 z^4 - 416821204800 z^5 + 20547541123200 z^6 - 101022333753600 z^7 + 166677884110080 z^8 - 129593688998400 z^9 + 55593056977920 z^10 - 14345641175040 z^11 + 2339615416320 z^12 - 247408140288 z^13 + 17072121600 z^14 - 758006016 z^15 + 20741632 z^16 - 316416 z^17 + 2048 z^18) - (1/281302875) ((128 Sqrt[Pi] (-22855996800 z^(11/2) + 346356259200 z^(13/2) - 1199060755200 z^(15/2) + 1676589062400 z^(17/2) - 1189793253600 z^(19/2) + 483130539360 z^(21/2) - 120390611040 z^(23/2) + 19184700960 z^(25/2) - 1996794585 z^(27/2) + 136258905 z^(29/2) - 6001728 z^(31/2) + 163272 z^(33/2) - 2480 z^(35/2) + 16 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]