Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a87w)

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=5, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.a87w.01

Input Form

HypergeometricPFQ[{-(5/2), 5}, {-(7/2), -(7/2)}, -z] == (1/4410) (4410 + 4500 z + 3240 z^2 + 1680 z^3 - 6720 z^4 + 36111 z^5 - 20585 z^6 + 3998 z^7 - 308 z^8 + 8 z^9) + (1/8820) ((Sqrt[Pi] (36465 z^(9/2) - 89505 z^(11/2) + 44880 z^(13/2) - 8296 z^(15/2) + 624 z^(17/2) - 16 z^(19/2)) 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]