Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3947)

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=3/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.3947.01

Input Form

HypergeometricPFQ[{-(9/2), 3/2}, {-(1/2), 11/2}, -z] == (1/(196608 z^4)) ((496125 - 434700 z + 234360 z^2 - 75600 z^3 + 98304 z^4 - 335424 z^5 - 203136 z^6 - 30464 z^7 - 1280 z^8)/E^z) + (1/(393216 z^(9/2))) (Sqrt[Pi] (-496125 + 765450 z - 612360 z^2 + 317520 z^3 - 846720 z^6 - 435456 z^7 - 62208 z^8 - 2560 z^9) Erf[Sqrt[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]