Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am1t)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.am1t.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(3/2), -(3/2)}, -z] == (1/2835) (2835 - 22680 z + 1247400 z^2 - 48898080 z^3 + 176132880 z^4 - 199051776 z^5 + 98742528 z^6 - 24818880 z^7 + 3356544 z^8 - 244704 z^9 + 8960 z^10 - 128 z^11) + (1/2835) ((16 Sqrt[Pi] (-498960 z^(5/2) + 5987520 z^(7/2) - 15384600 z^(9/2) + 14953680 z^(11/2) - 6858810 z^(13/2) + 1649088 z^(15/2) - 217161 z^(17/2) + 15570 z^(19/2) - 564 z^(21/2) + 8 z^(23/2)) 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]