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

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=-11/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(11/2), -(1/2)}, -z] == (1/3274425) (3274425 - 26790750 z - 196465500 z^2 - 567567000 z^3 - 1362160800 z^4 - 3969725760 z^5 - 27935107200 z^6 + 69154041600 z^7 - 52588327680 z^8 + 19097863680 z^9 - 3831504768 z^10 + 451604160 z^11 - 31787360 z^12 + 1303872 z^13 - 28544 z^14 + 256 z^15) - (1/3274425) ((16 Sqrt[Pi] (-3076768800 z^(13/2) + 5572370160 z^(15/2) - 3791521440 z^(17/2) + 1301382180 z^(19/2) - 252682290 z^(21/2) + 29180025 z^(23/2) - 2026584 z^(25/2) + 82376 z^(27/2) - 1792 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]