Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7466)

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=-15/4

http://functions.wolfram.com/07.22.03.7466.01

Input Form

HypergeometricPFQ[{5}, {-(15/4), 11/4}, z] == (1/(8110080 z^(7/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-467775 + 4680 z + 328080 z^2 - 22656 z^3 + 2048 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-1403325 + 2806650 Sqrt[z] - 3912300 z + 4082400 z^(3/2) - 1058400 z^2 - 2328480 z^(5/2) + 2479680 z^3 - 783360 z^(7/2) - 153600 z^4 + 122880 z^(9/2) + 16384 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (1403325 + 2806650 Sqrt[z] + 3912300 z + 4082400 z^(3/2) + 1058400 z^2 - 2328480 z^(5/2) - 2479680 z^3 - 783360 z^(7/2) + 153600 z^4 + 122880 z^(9/2) - 16384 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]