Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aia3)

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=2, a₂>=2

For fixed z and a₁=2, a₂=5, b₁>=-11/2

For fixed z and a₁=2, a₂=5, b₁=-9/2

http://functions.wolfram.com/07.25.03.aia3.01

Input Form

HypergeometricPFQ[{2, 5}, {-(9/2), 1}, -z] == (1/11340) (11340 + 25200 z + 32400 z^2 + 40320 z^3 + 67200 z^4 + 290304 z^5 - 310155 z^6 + 98440 z^7 - 13152 z^8 + 768 z^9 - 16 z^10) + (1/22680) ((Sqrt[Pi] (-818805 z^(11/2) + 707370 z^(13/2) - 209304 z^(15/2) + 27056 z^(17/2) - 1552 z^(19/2) + 32 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]