Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8788)

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`=-1/2

http://functions.wolfram.com/07.22.03.8788.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 3/4}, z] == (1/1703116800) ((4 (212889600 - 297868725 Sqrt[z] + 2441369700 z + 737936640 z^(3/2) - 3327448320 z^2 - 144990720 z^(5/2) + 598456320 z^3 + 6389760 z^(7/2) - 25755648 z^4 - 65536 z^(9/2) + 262144 z^5 + E^(4 Sqrt[z]) (212889600 + 297868725 Sqrt[z] + 2441369700 z - 737936640 z^(3/2) - 3327448320 z^2 + 144990720 z^(5/2) + 598456320 z^3 - 6389760 z^(7/2) - 25755648 z^4 + 65536 z^(9/2) + 262144 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (723647925 + 11578366800 z - 13722508800 z^2 + 2412748800 z^3 - 103219200 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (723647925 + 11578366800 z - 13722508800 z^2 + 2412748800 z^3 - 103219200 z^4 + 1048576 z^5) 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]