Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8za)

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

For fixed z and a₁=-11/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a8za.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(3/2), 21/4}, z] == -((221 (-4 z^(1/4) (-204622092675 - 272829456900 Sqrt[z] - 141615825120 z - 22525050240 z^(3/2) + 4810417920 z^2 - 2125347840 z^(5/2) - 738017280 z^3 + 2982346752 z^(7/2) - 331677696 z^4 + 1304690688 z^(9/2) - 65011712 z^5 + 310378496 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-204622092675 + 272829456900 Sqrt[z] - 141615825120 z + 22525050240 z^(3/2) + 4810417920 z^2 + 2125347840 z^(5/2) - 738017280 z^3 - 2982346752 z^(7/2) - 331677696 z^4 - 1304690688 z^(9/2) - 65011712 z^5 - 310378496 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-204622092675 + 76647740400 z - 21515155200 z^2 + 7649832960 z^3 - 11127029760 z^4 - 5086642176 z^5 - 1291845632 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-204622092675 + 76647740400 z - 21515155200 z^2 + 7649832960 z^3 - 11127029760 z^4 - 5086642176 z^5 - 1291845632 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(11544872091648 z^(17/4)))

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]