Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7506)

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=-11/4

http://functions.wolfram.com/07.22.03.7506.01

Input Form

HypergeometricPFQ[{5}, {-(11/4), 19/4}, z] == -((1/(2097152 z^(15/4))) ((5 (-16 E^(2 Sqrt[z]) z^(3/4) (-10405395 - 3700620 z - 671328 z^2 - 78272 z^3 + 9216 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (31216185 - 62432370 Sqrt[z] + 64615320 z - 45987480 z^(3/2) + 25431840 z^2 - 11745216 z^(5/2) + 4822272 z^3 - 1878912 z^(7/2) + 626688 z^4 - 77824 z^(9/2) - 65536 z^5 + 32768 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (-31216185 - 62432370 Sqrt[z] - 64615320 z - 45987480 z^(3/2) - 25431840 z^2 - 11745216 z^(5/2) - 4822272 z^3 - 1878912 z^(7/2) - 626688 z^4 - 77824 z^(9/2) + 65536 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]