Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aan6)

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.aan6.01

Input Form

HypergeometricPFQ[{-(3/4)}, {-(9/2), 17/4}, z] == (1/(15032385536 z^(13/4))) ((13 (-4 z^(1/4) (-19010843775 - 25347791700 Sqrt[z] - 15917322960 z - 5773014720 z^(3/2) - 1273662720 z^2 - 248355840 z^(5/2) - 6811648 z^3 - 6307840 z^(7/2) + E^(4 Sqrt[z]) (-19010843775 + 25347791700 Sqrt[z] - 15917322960 z + 5773014720 z^(3/2) - 1273662720 z^2 + 248355840 z^(5/2) - 6811648 z^3 + 6307840 z^(7/2))) + 385 E^(2 Sqrt[z]) Sqrt[2 Pi] (-49378815 + 11327040 z - 2013696 z^2 + 933888 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + 385 E^(2 Sqrt[z]) Sqrt[2 Pi] (-49378815 + 11327040 z - 2013696 z^2 + 933888 z^3 + 65536 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]