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

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=3, a₂>=3

For fixed z and a₁=3, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(7/2), -(7/2)}, -z] == (1/10418625) (10418625 - 14033250 z + 29189160 z^2 - 162162000 z^3 + 8270262000 z^4 - 333703450080 z^5 + 1323867767040 z^6 - 1737376252416 z^7 + 1053892373760 z^8 - 343725242880 z^9 + 65139554304 z^10 - 7440003072 z^11 + 514764800 z^12 - 20932608 z^13 + 456704 z^14 - 4096 z^15) + (1/10418625) ((1024 Sqrt[Pi] (-51891840 z^(9/2) + 655724160 z^(11/2) - 1863025920 z^(13/2) + 2098172160 z^(15/2) - 1172374560 z^(17/2) + 364385952 z^(19/2) - 67017888 z^(21/2) + 7507296 z^(23/2) - 512703 z^(25/2) + 20663 z^(27/2) - 448 z^(29/2) + 4 z^(31/2)) 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]