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

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=-5/2

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

Input Form

HypergeometricPFQ[{5/2, 3}, {-(5/2), -(5/2)}, -z] == (1/675) (675 - 810 z + 2520 z^2 - 75600 z^3 + 1734480 z^4 - 3754080 z^5 + 2539776 z^6 - 724992 z^7 + 96320 z^8 - 5824 z^9 + 128 z^10) - ((32/675) Sqrt[Pi] (-11880 z^(7/2) + 91080 z^(9/2) - 148680 z^(11/2) + 89400 z^(13/2) - 24075 z^(15/2) + 3099 z^(17/2) - 184 z^(19/2) + 4 z^(21/2)) 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]