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

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.acwm.01

Input Form

HypergeometricPFQ[{7/4}, {-(7/2), 23/4}, z] == (1/(4294967296 z^(19/4))) ((209 (4 z^(1/4) (5771092201875 + 7694789602500 Sqrt[z] + 5596210620000 z + 2771456688000 z^(3/2) + 994525459200 z^2 + 264826598400 z^(5/2) + 52407828480 z^3 + 7486832640 z^(7/2) + 704643072 z^4 + 33554432 z^(9/2) + E^(4 Sqrt[z]) (-5771092201875 + 7694789602500 Sqrt[z] - 5596210620000 z + 2771456688000 z^(3/2) - 994525459200 z^2 + 264826598400 z^(5/2) - 52407828480 z^3 + 7486832640 z^(7/2) - 704643072 z^4 + 33554432 z^(9/2))) + 208845 E^(2 Sqrt[z]) Sqrt[2 Pi] (-27633375 + 2679600 z - 134400 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] - 208845 E^(2 Sqrt[z]) Sqrt[2 Pi] (-27633375 + 2679600 z - 134400 z^2 + 4096 z^3) 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]