Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7402)

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=-21/4

http://functions.wolfram.com/07.22.03.7402.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 5/4}, z] == (1/(160392960 z^(1/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-15969555 + 11793060 z + 3572640 z^2 - 749760 z^3 + 54272 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (36018675 - 72037350 Sqrt[z] + 30561300 z + 34927200 z^(3/2) - 43797600 z^2 + 15412320 z^(5/2) + 2295360 z^3 - 2964480 z^(7/2) + 288768 z^4 + 221184 z^(9/2) + 16384 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (36018675 + 72037350 Sqrt[z] + 30561300 z - 34927200 z^(3/2) - 43797600 z^2 - 15412320 z^(5/2) + 2295360 z^3 + 2964480 z^(7/2) + 288768 z^4 - 221184 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]