Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amt7)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-1/2

http://functions.wolfram.com/07.25.03.amt7.01

Input Form

HypergeometricPFQ[{9/2, 5}, {-(1/2), 1/2}, -z] == (1/630) (630 + 56700 z - 831600 z^2 + 1940400 z^3 - 1580040 z^4 + 579612 z^5 - 106495 z^6 + 10050 z^7 - 460 z^8 + 8 z^9) + (1/1260) ((Sqrt[Pi] (-415800 z^(3/2) + 2827440 z^(5/2) - 5072760 z^(7/2) + 3654420 z^(9/2) - 1256745 z^(11/2) + 222600 z^(13/2) - 20552 z^(15/2) + 928 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]