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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), 3/2}, -z] == (1/1488375) (1488375 + 9355500 z + 34054020 z^2 + 129729600 z^3 + 1102701600 z^4 - 3428399520 z^5 + 3106071360 z^6 - 1306894176 z^7 + 298011960 z^8 - 39355050 z^9 + 3068904 z^10 - 138192 z^11 + 3296 z^12 - 32 z^13) + (1/1488375) ((Sqrt[Pi] z^(9/2) (-2095133040 + 4571199360 z - 3648168720 z^2 + 1439488260 z^3 - 316313235 z^4 + 40824378 z^5 - 3136392 z^6 + 139824 z^7 - 3312 z^8 + 32 z^9) 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]