Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9760)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9760.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 15/4}, z] == (11 (4 z^(1/4) (-31621769668125 - 42162359557500 Sqrt[z] - 16283394036000 z + 3987769968000 z^(3/2) - 1122483398400 z^2 + 3700655078400 z^(5/2) - 182496706560 z^3 + 678693765120 z^(7/2) - 14333706240 z^4 + 55242915840 z^(9/2) - 639631360 z^5 + 2508193792 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (31621769668125 - 42162359557500 Sqrt[z] + 16283394036000 z + 3987769968000 z^(3/2) + 1122483398400 z^2 + 3700655078400 z^(5/2) + 182496706560 z^3 + 678693765120 z^(7/2) + 14333706240 z^4 + 55242915840 z^(9/2) + 639631360 z^5 + 2508193792 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (31621769668125 - 17446493610000 z + 11165755910400 z^2 + 14178737664000 z^3 + 2668938854400 z^4 + 218989854720 z^5 + 9982443520 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (31621769668125 - 17446493610000 z + 11165755910400 z^2 + 14178737664000 z^3 + 2668938854400 z^4 + 218989854720 z^5 + 9982443520 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (974098582732800 z^(11/4))

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]