Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ak1k)

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, a₂>=3

For fixed z and a₁=3, a₂=7/2, b₁>=-11/2

For fixed z and a₁=3, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ak1k.01

Input Form

HypergeometricPFQ[{3, 7/2}, {-(9/2), -(7/2)}, -z] == (1/1488375) (1488375 - 992250 z + 1020600 z^2 - 2494800 z^3 + 32432400 z^4 + 1362160800 z^5 - 12532665600 z^6 + 22350343680 z^7 - 15534408960 z^8 + 5283540480 z^9 - 972871680 z^10 + 100823040 z^11 - 5820416 z^12 + 173056 z^13 - 2048 z^14) + (1/1488375) ((512 Sqrt[Pi] (-7862400 z^(11/2) + 38404800 z^(13/2) - 55339200 z^(15/2) + 34750800 z^(17/2) - 11183760 z^(19/2) + 1993320 z^(21/2) - 202440 z^(23/2) + 11535 z^(25/2) - 340 z^(27/2) + 4 z^(29/2)) 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]