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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 6}, {-(11/2), 3/2}, -z] == (1/623700) (-56700 + 37800 z^2 + 41400 z^3 + 37170 z^4 + 43470 z^5 + 136395 z^6 - 71208 z^7 + 11520 z^8 - 736 z^9 + 16 z^10) + (1/(1247400 Sqrt[z])) ((Sqrt[Pi] (680400 + 680400 z + 340200 z^2 + 113400 z^3 + 28350 z^4 + 5670 z^5 + 945 z^6 - 334170 z^7 + 153240 z^8 - 23760 z^9 + 1488 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]