Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8by)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8by.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(3/4)}, z] == (1/(16242969600 z^(9/2))) ((-75983032125 + 75983032125 E^(4 Sqrt[z]) - 151966064250 Sqrt[z] - 151966064250 E^(4 Sqrt[z]) Sqrt[z] - 117851233500 z + 117851233500 E^(4 Sqrt[z]) z - 33081048000 z^(3/2) - 33081048000 E^(4 Sqrt[z]) z^(3/2) + 5935129200 z^2 - 5935129200 E^(4 Sqrt[z]) z^2 + 1945944000 z^(5/2) + 1945944000 E^(4 Sqrt[z]) z^(5/2) - 2315174400 z^3 + 2315174400 E^(4 Sqrt[z]) z^3 + 1596672000 z^(7/2) + 1596672000 E^(4 Sqrt[z]) z^(7/2) - 1064448000 z^4 + 1064448000 E^(4 Sqrt[z]) z^4 + 802897920 z^(9/2) + 802897920 E^(4 Sqrt[z]) z^(9/2) - 778567680 z^5 + 778567680 E^(4 Sqrt[z]) z^5 + 1179648000 z^(11/2) + 1179648000 E^(4 Sqrt[z]) z^(11/2) - 5080350720 z^6 + 5080350720 E^(4 Sqrt[z]) z^6 - 127795200 z^(13/2) - 127795200 E^(4 Sqrt[z]) z^(13/2) + 517472256 z^7 - 517472256 E^(4 Sqrt[z]) z^7 + 2097152 z^(15/2) + 2097152 E^(4 Sqrt[z]) z^(15/2) - 8388608 z^8 + 8388608 E^(4 Sqrt[z]) z^8 - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (157905 - 15840 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (157905 - 15840 z + 256 z^2) 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]