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

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.ajhx.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(7/2), 7/2}, -z] == (-6480 - 2160 z - 144 z^2 + 360 z^3 + 450 z^4 + 606 z^5 + 2067 z^6 - 1242 z^7 + 188 z^8 - 8 z^9)/(504 z^2) + (1/(1008 z^(5/2))) ((Sqrt[Pi] (6480 + 6480 z + 3240 z^2 + 1080 z^3 + 270 z^4 + 54 z^5 + 9 z^6 - 5208 z^7 + 2664 z^8 - 384 z^9 + 16 z^10) 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]