Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7380)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-23/4

http://functions.wolfram.com/07.22.03.7380.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 7/4}, z] == (1/(775272960 z^(3/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (22103235 + 37313100 z - 2052000 z^2 - 582208 z^3 + 39936 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-79053975 + 158107950 Sqrt[z] + 48648600 z - 308107800 z^(3/2) + 281867040 z^2 - 96707520 z^(5/2) - 10832640 z^3 + 19643520 z^(7/2) - 4853760 z^4 - 569344 z^(9/2) + 327680 z^5 + 32768 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (79053975 + 158107950 Sqrt[z] - 48648600 z - 308107800 z^(3/2) - 281867040 z^2 - 96707520 z^(5/2) + 10832640 z^3 + 19643520 z^(7/2) + 4853760 z^4 - 569344 z^(9/2) - 327680 z^5 + 32768 z^(11/2)) 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]