Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akm2)

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=-11/2

http://functions.wolfram.com/07.25.03.akm2.01

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(7/2)}, -z] == (1/1031443875) (1031443875 - 884094750 z + 1021620600 z^2 - 2432430000 z^3 + 24810786000 z^4 + 439977938400 z^5 + 8212921516800 z^6 - 55454829534720 z^7 + 91784809670400 z^8 - 66264149952000 z^9 + 25429848238080 z^10 - 5713255895040 z^11 + 790007844864 z^12 - 68638187520 z^13 + 3728670720 z^14 - 122052608 z^15 + 2187264 z^16 - 16384 z^17) + (1/1031443875) ((4096 Sqrt[Pi] (-5089392000 z^(13/2) + 20696860800 z^(15/2) - 28520553600 z^(17/2) + 18764887680 z^(19/2) - 6826770720 z^(21/2) + 1483907040 z^(23/2) - 200831400 z^(25/2) + 17198280 z^(27/2) - 924957 z^(29/2) + 30063 z^(31/2) - 536 z^(33/2) + 4 z^(35/2)) 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]