Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aiu3)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-9/2

http://functions.wolfram.com/07.25.03.aiu3.01

Input Form

HypergeometricPFQ[{5/2, 3}, {-(9/2), -(9/2)}, -z] == (1/2679075) (2679075 - 992250 z + 567000 z^2 - 680400 z^3 + 2494800 z^4 - 90810720 z^5 + 2626041600 z^6 - 7450329600 z^7 + 6925121280 z^8 - 2907025920 z^9 + 630915072 z^10 - 74803200 z^11 + 4838400 z^12 - 158720 z^13 + 2048 z^14) - (1/2679075) ((512 Sqrt[Pi] (-982800 z^(11/2) + 9298800 z^(13/2) - 19512360 z^(15/2) + 15893640 z^(17/2) - 6231330 z^(19/2) + 1300950 z^(21/2) - 150675 z^(23/2) + 9603 z^(25/2) - 312 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]