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

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=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(7/2), -(5/2)}, -z] == (1/70875) (70875 - 121500 z + 396900 z^2 - 6350400 z^3 - 314344800 z^4 + 3453278400 z^5 - 7310815200 z^6 + 6063353280 z^7 - 2493740880 z^8 + 568046040 z^9 - 75547980 z^10 + 5950560 z^11 - 270848 z^12 + 6528 z^13 - 64 z^14) + (1/70875) ((2 Sqrt[Pi] (498841200 z^(9/2) - 2834325000 z^(11/2) + 4779108000 z^(13/2) - 3549156300 z^(15/2) + 1373155650 z^(17/2) - 301577265 z^(19/2) + 39197850 z^(21/2) - 3041400 z^(23/2) + 137040 z^(25/2) - 3280 z^(27/2) + 32 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]