Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amr7)

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=-7/2

http://functions.wolfram.com/07.25.03.amr7.01

Input Form

HypergeometricPFQ[{9/2, 5}, {-(7/2), -(5/2)}, -z] == (1/496125) (496125 - 1275750 z + 5613300 z^2 - 113513400 z^3 - 6810804000 z^4 + 91891800000 z^5 - 236624169600 z^6 + 238858018560 z^7 - 120462554880 z^8 + 34137830400 z^9 - 5782129920 z^10 + 601870080 z^11 - 38495456 z^12 + 1462848 z^13 - 30080 z^14 + 256 z^15) - (1/496125) ((16 Sqrt[Pi] (-1470268800 z^(9/2) + 9957729600 z^(11/2) - 20074824000 z^(13/2) + 17946961200 z^(15/2) - 8452710000 z^(17/2) + 2298121560 z^(19/2) - 379094520 z^(21/2) + 38776425 z^(23/2) - 2450760 z^(25/2) + 92360 z^(27/2) - 1888 z^(29/2) + 16 z^(31/2)) 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]