Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9470)

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`=3/2

http://functions.wolfram.com/07.22.03.9470.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, 13/4}, z] == (4 z^(1/4) (206239658625 + 274986211500 Sqrt[z] - 1319933815200 z + 14640397833600 z^(3/2) + 6686560177920 z^2 - 31489397775360 z^(5/2) - 1964803276800 z^3 + 8242899517440 z^(7/2) + 137343467520 z^4 - 557939687424 z^(9/2) - 2912944128 z^5 + 11702108160 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (206239658625 - 274986211500 Sqrt[z] - 1319933815200 z - 14640397833600 z^(3/2) + 6686560177920 z^2 + 31489397775360 z^(5/2) - 1964803276800 z^3 - 8242899517440 z^(7/2) + 137343467520 z^4 + 557939687424 z^(9/2) - 2912944128 z^5 - 11702108160 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (206239658625 - 1539922784400 z - 73916293651200 z^2 + 131406744268800 z^3 - 33373141401600 z^4 + 2240434667520 z^5 - 46858764288 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (206239658625 - 1539922784400 z - 73916293651200 z^2 + 131406744268800 z^3 - 33373141401600 z^4 + 2240434667520 z^5 - 46858764288 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(392429819658240 z^(9/4))

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]