Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7524)

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=-9/4

http://functions.wolfram.com/07.22.03.7524.01

Input Form

HypergeometricPFQ[{5}, {-(9/4), 21/4}, z] == -((1/(25165824 z^(17/4))) ((221 (8 E^(2 Sqrt[z]) z^(1/4) (79053975 + 34428240 z + 7176960 z^2 + 860160 z^3 + 96768 z^4 + 8192 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-79053975 + 158107950 Sqrt[z] - 160914600 z + 111018600 z^(3/2) - 58514400 z^2 + 25220160 z^(5/2) - 9327360 z^3 + 3085440 z^(7/2) - 983040 z^4 + 348160 z^(9/2) - 131072 z^5 + 32768 z^(11/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (79053975 + 158107950 Sqrt[z] + 160914600 z + 111018600 z^(3/2) + 58514400 z^2 + 25220160 z^(5/2) + 9327360 z^3 + 3085440 z^(7/2) + 983040 z^4 + 348160 z^(9/2) + 131072 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]