Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8298)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8298.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(7/4)}, z] == (1/(1315723500 Sqrt[z])) ((-204417675 + 204417675 E^(4 Sqrt[z]) + 249026400 Sqrt[z] + 249026400 E^(4 Sqrt[z]) Sqrt[z] - 228765600 z + 228765600 E^(4 Sqrt[z]) z + 212889600 z^(3/2) + 212889600 E^(4 Sqrt[z]) z^(3/2) - 238291200 z^2 + 238291200 E^(4 Sqrt[z]) z^2 + 397393920 z^(5/2) + 397393920 E^(4 Sqrt[z]) z^(5/2) - 1811496960 z^3 + 1811496960 E^(4 Sqrt[z]) z^3 - 84908160 z^(7/2) - 84908160 E^(4 Sqrt[z]) z^(7/2) + 349800960 z^4 - 349800960 E^(4 Sqrt[z]) z^4 + 3502080 z^(9/2) + 3502080 E^(4 Sqrt[z]) z^(9/2) - 14106624 z^5 + 14106624 E^(4 Sqrt[z]) z^5 - 32768 z^(11/2) - 32768 E^(4 Sqrt[z]) z^(11/2) + 131072 z^6 - 131072 E^(4 Sqrt[z]) z^6 + 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-58503375 + 11012400 z - 441600 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 32 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-58503375 + 11012400 z - 441600 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]