Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8940)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8940.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 11/4}, z] == (-4 z^(1/4) (8875936517175 + 34828516768500 Sqrt[z] + 95396900770080 z - 507030136583040 z^(3/2) - 59874855264000 z^2 + 259519411952640 z^(5/2) + 7579040071680 z^3 - 31178915905536 z^(7/2) - 301272072192 z^4 + 1217353482240 z^(9/2) + 4146069504 z^5 - 16634609664 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-8875936517175 + 34828516768500 Sqrt[z] - 95396900770080 z - 507030136583040 z^(3/2) + 59874855264000 z^2 + 259519411952640 z^(5/2) - 7579040071680 z^3 - 31178915905536 z^(7/2) + 301272072192 z^4 + 1217353482240 z^(9/2) - 4146069504 z^5 - 16634609664 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (25614965601225 + 318764016370800 z - 2185810397971200 z^2 + 1059786859622400 z^3 - 125604368547840 z^4 + 4881789222912 z^5 - 66588770304 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (25614965601225 + 318764016370800 z - 2185810397971200 z^2 + 1059786859622400 z^3 - 125604368547840 z^4 + 4881789222912 z^5 - 66588770304 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(6859118975385600 z^(7/4))

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]