Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a97a)

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`=9/2

http://functions.wolfram.com/07.22.03.a97a.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, 21/4}, z] == (4 z^(1/4) (-705556726875 + 2111243003100 Sqrt[z] - 727265800800 z + 1929039235200 z^(3/2) - 369634003200 z^2 + 1109385446400 z^(5/2) - 250301399040 z^3 + 1143661854720 z^(7/2) + 53804728320 z^4 - 221054238720 z^(9/2) - 2002780160 z^5 + 8061452288 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-705556726875 - 2111243003100 Sqrt[z] - 727265800800 z - 1929039235200 z^(3/2) - 369634003200 z^2 - 1109385446400 z^(5/2) - 250301399040 z^3 - 1143661854720 z^(7/2) + 53804728320 z^4 + 221054238720 z^(9/2) - 2002780160 z^5 - 8061452288 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-705556726875 - 6078642570000 z - 6483885408000 z^2 - 3842302464000 z^3 - 4728987648000 z^4 + 890162380800 z^5 - 32296140800 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-705556726875 - 6078642570000 z - 6483885408000 z^2 - 3842302464000 z^3 - 4728987648000 z^4 + 890162380800 z^5 - 32296140800 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(13529146982400 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]