Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9286)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.9286.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(5/2), 21/4}, z] == (221 (-4 z^(1/4) (7872835015670625 + 10497113354227500 Sqrt[z] + 5167809651312000 z + 492172347744000 z^(3/2) - 313849033344000 z^2 + 138335662080000 z^(5/2) + 36404121600000 z^3 - 169109279539200 z^(7/2) + 20773689753600 z^4 - 78828915916800 z^(9/2) + 4243335413760 z^5 - 16880479764480 z^(11/2) + 661357854720 z^6 - 3277596917760 z^(13/2) - 225485783040 z^7 + 914828034048 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (7872835015670625 - 10497113354227500 Sqrt[z] + 5167809651312000 z - 492172347744000 z^(3/2) - 313849033344000 z^2 - 138335662080000 z^(5/2) + 36404121600000 z^3 + 169109279539200 z^(7/2) + 20773689753600 z^4 + 78828915916800 z^(9/2) + 4243335413760 z^5 + 16880479764480 z^(11/2) + 661357854720 z^6 + 3277596917760 z^(13/2) - 225485783040 z^7 - 914828034048 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (7872835015670625 - 3229881032070000 z + 998610560640000 z^2 - 392436430848000 z^3 + 627898289356800 z^4 + 304435534233600 z^5 + 66271680921600 z^6 + 13770738892800 z^7 - 3672197038080 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (7872835015670625 - 3229881032070000 z + 998610560640000 z^2 - 392436430848000 z^3 + 627898289356800 z^4 + 304435534233600 z^5 + 66271680921600 z^6 + 13770738892800 z^7 - 3672197038080 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (664984632478924800 z^(17/4))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]