Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7398)

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/07.22.03.7398.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), -(3/4)}, z] == (1/7518420) ((-4 E^(2 Sqrt[z]) (-1879605 - 2386800 z - 8402850 z^2 + 691560 z^3 + 265952 z^4 + 46592 z^5) - E^(4 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (7571025 - 15142050 Sqrt[z] + 9832500 z + 524400 z^(3/2) - 3377136 z^2 + 671232 z^(5/2) + 624128 z^3 + 94208 z^(7/2) + 4096 z^4) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] z^(7/4) (-7571025 - 15142050 Sqrt[z] - 9832500 z + 524400 z^(3/2) + 3377136 z^2 + 671232 z^(5/2) - 624128 z^3 + 94208 z^(7/2) - 4096 z^4) 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]