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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=4, b₁>=-11/2

For fixed z and a₁=3/2, a₂=4, b₁=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 4}, {-(5/2), -(5/2)}, -z] == (1/675) (675 - 648 z + 1800 z^2 - 50400 z^3 + 1093392 z^4 - 2255616 z^5 + 1462656 z^6 - 401664 z^7 + 51472 z^8 - 3008 z^9 + 64 z^10) - ((8/675) Sqrt[Pi] (-30888 z^(7/2) + 226512 z^(9/2) - 354744 z^(11/2) + 205152 z^(13/2) - 53247 z^(15/2) + 6618 z^(17/2) - 380 z^(19/2) + 8 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]