Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8310)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8310.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 5/4}, z] == (1/(61590896640000 Sqrt[z])) ((-4 (-1116393062400 - 2025794624175 Sqrt[z] + 11517178862700 z + 1772145118800 z^(3/2) - 7827650913600 z^2 - 287122429440 z^(5/2) + 1187937515520 z^3 + 13887774720 z^(7/2) - 56215633920 z^4 - 225116160 z^(9/2) + 903610368 z^5 + 1048576 z^(11/2) - 4194304 z^6 + E^(4 Sqrt[z]) (1116393062400 - 2025794624175 Sqrt[z] - 11517178862700 z + 1772145118800 z^(3/2) + 7827650913600 z^2 - 287122429440 z^(5/2) - 1187937515520 z^3 + 13887774720 z^(7/2) + 56215633920 z^4 - 225116160 z^(9/2) - 903610368 z^5 + 1048576 z^(11/2) + 4194304 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (7905853580625 - 50597462916000 z + 32125373280000 z^2 - 4792596480000 z^3 + 225533952000 z^4 - 3617587200 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (7905853580625 - 50597462916000 z + 32125373280000 z^2 - 4792596480000 z^3 + 225533952000 z^4 - 3617587200 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[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,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]