Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7880)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=1/4

http://functions.wolfram.com/07.22.03.7880.01

Input Form

HypergeometricPFQ[{6}, {1/4, 19/4}, z] == (1/(67108864 z^(15/4))) ((231 (48 E^(2 Sqrt[z]) z^(3/4) (-13475 - 7000 z - 2560 z^2 + 4096 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-121275 + 242550 Sqrt[z] - 270900 z + 218400 z^(3/2) - 148080 z^2 + 91200 z^(5/2) - 64000 z^3 + 51200 z^(7/2) + 102400 z^4 + 16384 z^(9/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (121275 + 242550 Sqrt[z] + 270900 z + 218400 z^(3/2) + 148080 z^2 + 91200 z^(5/2) + 64000 z^3 + 51200 z^(7/2) - 102400 z^4 + 16384 z^(9/2)) 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]