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

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.acfz.01

Input Form

HypergeometricPFQ[{-(1/2), 6}, {-(11/2), -(11/2)}, -z] == (1/1620840375) (1620840375 + 160744500 z - 13891500 z^2 + 4536000 z^3 - 4082400 z^4 + 12700800 z^5 - 419126400 z^6 + 11313993600 z^7 - 30772425600 z^8 + 28163560320 z^9 - 11982476160 z^10 + 2729704080 z^11 - 355990320 z^12 + 27162240 z^13 - 1188352 z^14 + 27392 z^15 - 256 z^16) + (1/1620840375) ((8 Sqrt[Pi] (280816200 z^(13/2) - 2527345800 z^(15/2) + 5137284600 z^(17/2) - 4141531800 z^(19/2) + 1649795175 z^(21/2) - 361935315 z^(23/2) + 46126290 z^(25/2) - 3467880 z^(27/2) + 150240 z^(29/2) - 3440 z^(31/2) + 32 z^(33/2)) 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]