Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9374)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.9374.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 13/4}, z] == (1/(4396972769280 z^(9/4))) ((-4 z^(1/4) (44483063625 + 59310751500 Sqrt[z] - 43135092000 z - 93664771200 z^(3/2) - 13048439040 z^2 - 321880366080 z^(5/2) - 226034565120 z^3 + 1020060303360 z^(7/2) + 44253511680 z^4 - 182232809472 z^(9/2) - 1797259264 z^5 + 7239368704 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (44483063625 - 59310751500 Sqrt[z] - 43135092000 z + 93664771200 z^(3/2) - 13048439040 z^2 + 321880366080 z^(5/2) - 226034565120 z^3 - 1020060303360 z^(7/2) + 44253511680 z^4 + 182232809472 z^(9/2) - 1797259264 z^5 - 7239368704 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (44483063625 - 90583693200 z + 621145324800 z^2 + 1840430592000 z^3 - 4206698496000 z^4 + 734260101120 z^5 - 29007806464 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (44483063625 - 90583693200 z + 621145324800 z^2 + 1840430592000 z^3 - 4206698496000 z^4 + 734260101120 z^5 - 29007806464 z^6 + 268435456 z^7) 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]