Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9422)

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/07.22.03.9422.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 13/4}, z] == (4 z^(1/4) (-68746552875 - 91662070500 Sqrt[z] + 146659312800 z + 251415964800 z^(3/2) + 1367991555840 z^2 - 7271611038720 z^(5/2) - 820855848960 z^3 + 3514400440320 z^(7/2) + 84522762240 z^4 - 344983339008 z^(9/2) - 2355101696 z^5 + 9470738432 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-68746552875 + 91662070500 Sqrt[z] + 146659312800 z - 251415964800 z^(3/2) + 1367991555840 z^2 + 7271611038720 z^(5/2) - 820855848960 z^3 - 3514400440320 z^(7/2) + 84522762240 z^4 + 344983339008 z^(9/2) - 2355101696 z^5 - 9470738432 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-68746552875 + 219988969200 z - 3519823507200 z^2 + 31287320064000 z^3 - 14302774886400 z^4 + 1386935746560 z^5 - 37933285376 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-68746552875 + 219988969200 z - 3519823507200 z^2 + 31287320064000 z^3 - 14302774886400 z^4 + 1386935746560 z^5 - 37933285376 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(37374268538880 z^(9/4))

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]