Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9816)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.9816.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(7/2), 23/4}, z] == (209 (4 z^(1/4) (-172180535842940625 - 229574047790587500 Sqrt[z] - 133570355078160000 z - 38162958593760000 z^(3/2) - 3264654347136000 z^2 + 170144851968000 z^(5/2) - 225114727219200 z^3 + 275721913958400 z^(7/2) - 61508775444480 z^4 + 200119568302080 z^(9/2) - 8802627747840 z^5 + 32146068602880 z^(11/2) - 721755832320 z^6 + 2707440009216 z^(13/2) - 45097156608 z^7 + 167503724544 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (172180535842940625 - 229574047790587500 Sqrt[z] + 133570355078160000 z - 38162958593760000 z^(3/2) + 3264654347136000 z^2 + 170144851968000 z^(5/2) + 225114727219200 z^3 + 275721913958400 z^(7/2) + 61508775444480 z^4 + 200119568302080 z^(9/2) + 8802627747840 z^5 + 32146068602880 z^(11/2) + 721755832320 z^6 + 2707440009216 z^(13/2) + 45097156608 z^7 + 167503724544 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (172180535842940625 - 50088883154310000 z + 10049180319360000 z^2 - 2143825134796800 z^3 + 816695289446400 z^4 + 768654390067200 z^5 + 126138156318720 z^6 + 10678362439680 z^7 + 657129996288 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (172180535842940625 - 50088883154310000 z + 10049180319360000 z^2 - 2143825134796800 z^3 + 816695289446400 z^4 + 768654390067200 z^5 + 126138156318720 z^6 + 10678362439680 z^7 + 657129996288 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (1063975411966279680 z^(19/4))

Standard Form

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MathML 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]