Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vw)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7vw.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(5/4)}, z] == (1/(240334617600 z^(9/2))) ((-1581170716125 + 1581170716125 E^(4 Sqrt[z]) - 3162341432250 Sqrt[z] - 3162341432250 E^(4 Sqrt[z]) Sqrt[z] - 2474875903500 z + 2474875903500 E^(4 Sqrt[z]) z - 733296564000 z^(3/2) - 733296564000 E^(4 Sqrt[z]) z^(3/2) + 96486390000 z^2 - 96486390000 E^(4 Sqrt[z]) z^2 + 46313467200 z^(5/2) + 46313467200 E^(4 Sqrt[z]) z^(5/2) - 41167526400 z^3 + 41167526400 E^(4 Sqrt[z]) z^3 + 23524300800 z^(7/2) + 23524300800 E^(4 Sqrt[z]) z^(7/2) - 12831436800 z^4 + 12831436800 E^(4 Sqrt[z]) z^4 + 7595212800 z^(9/2) + 7595212800 E^(4 Sqrt[z]) z^(9/2) - 5339873280 z^5 + 5339873280 E^(4 Sqrt[z]) z^5 + 4954521600 z^(11/2) + 4954521600 E^(4 Sqrt[z]) z^(11/2) - 7303331840 z^6 + 7303331840 E^(4 Sqrt[z]) z^6 + 30974935040 z^(13/2) + 30974935040 E^(4 Sqrt[z]) z^(13/2) + 616038400 z^7 - 616038400 E^(4 Sqrt[z]) z^7 - 2489319424 z^(15/2) - 2489319424 E^(4 Sqrt[z]) z^(15/2) - 8388608 z^8 + 8388608 E^(4 Sqrt[z]) z^8 + 33554432 z^(17/2) + 33554432 E^(4 Sqrt[z]) z^(17/2) + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (239785 - 19040 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (239785 - 19040 z + 256 z^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]