Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8924)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8924.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(5/4)}, z] == (1/(3270682800 z^(3/2))) ((144729585 - 144729585 E^(4 Sqrt[z]) + 289459170 Sqrt[z] + 289459170 E^(4 Sqrt[z]) Sqrt[z] - 421031520 z + 421031520 E^(4 Sqrt[z]) z + 407332800 z^(3/2) + 407332800 E^(4 Sqrt[z]) z^(3/2) - 388281600 z^2 + 388281600 E^(4 Sqrt[z]) z^2 + 440391168 z^(5/2) + 440391168 E^(4 Sqrt[z]) z^(5/2) - 740081664 z^3 + 740081664 E^(4 Sqrt[z]) z^3 + 3387654144 z^(7/2) + 3387654144 E^(4 Sqrt[z]) z^(7/2) + 163973376 z^4 - 163973376 E^(4 Sqrt[z]) z^4 - 675935232 z^(9/2) - 675935232 E^(4 Sqrt[z]) z^(9/2) - 6905856 z^5 + 6905856 E^(4 Sqrt[z]) z^5 + 27820032 z^(11/2) + 27820032 E^(4 Sqrt[z]) z^(11/2) + 65536 z^6 - 65536 E^(4 Sqrt[z]) z^6 - 262144 z^(13/2) - 262144 E^(4 Sqrt[z]) z^(13/2) - 64 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-54759159 + 10641456 z - 435456 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 64 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-54759159 + 10641456 z - 435456 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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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]