Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9sm)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.a9sm.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(7/2), 21/4}, z] == (221 (-4 z^(1/4) (741422907225 + 988563876300 Sqrt[z] + 614234229840 z + 216425753280 z^(3/2) + 41532480000 z^2 + 4148213760 z^(5/2) + 245145600 z^3 - 875986944 z^(7/2) + 31260672 z^4 - 121896960 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (741422907225 - 988563876300 Sqrt[z] + 614234229840 z - 216425753280 z^(3/2) + 41532480000 z^2 - 4148213760 z^(5/2) + 245145600 z^3 + 875986944 z^(7/2) + 31260672 z^4 + 121896960 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (741422907225 - 176616871200 z + 29072736000 z^2 - 5393203200 z^3 + 3406233600 z^4 + 484442112 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (741422907225 - 176616871200 z + 29072736000 z^2 - 5393203200 z^3 + 3406233600 z^4 + 484442112 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(2748779069440 z^(17/4))

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]