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

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.ajtc.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(7/2), 7/2}, -z] == (1/(5040 z^2)) (-32400 - 10800 z + 1800 z^2 + 5400 z^3 + 6570 z^4 + 9750 z^5 + 37215 z^6 - 30048 z^7 + 6800 z^8 - 576 z^9 + 16 z^10) + (1/(10080 z^(5/2))) ((Sqrt[Pi] (32400 + 32400 z + 16200 z^2 + 5400 z^3 + 1350 z^4 + 270 z^5 + 45 z^6 - 98970 z^7 + 66360 z^8 - 14160 z^9 + 1168 z^10 - 32 z^11) 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]