Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9642)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9642.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(7/4)}, z] == (1/(4206929126400 z^(9/2))) ((-36091940259375 + 36091940259375 E^(4 Sqrt[z]) - 72183880518750 Sqrt[z] - 72183880518750 E^(4 Sqrt[z]) Sqrt[z] - 56922145780500 z + 56922145780500 E^(4 Sqrt[z]) z - 17599117536000 z^(3/2) - 17599117536000 E^(4 Sqrt[z]) z^(3/2) + 1665630766800 z^2 - 1665630766800 E^(4 Sqrt[z]) z^2 + 1131371841600 z^(5/2) + 1131371841600 E^(4 Sqrt[z]) z^(5/2) - 808474867200 z^3 + 808474867200 E^(4 Sqrt[z]) z^3 + 394377984000 z^(7/2) + 394377984000 E^(4 Sqrt[z]) z^(7/2) - 182020608000 z^4 + 182020608000 E^(4 Sqrt[z]) z^4 + 88732385280 z^(9/2) + 88732385280 E^(4 Sqrt[z]) z^(9/2) - 49049763840 z^5 + 49049763840 E^(4 Sqrt[z]) z^5 + 32982958080 z^(11/2) + 32982958080 E^(4 Sqrt[z]) z^(11/2) - 29711400960 z^6 + 29711400960 E^(4 Sqrt[z]) z^6 + 42970644480 z^(13/2) + 42970644480 E^(4 Sqrt[z]) z^(13/2) - 180287963136 z^7 + 180287963136 E^(4 Sqrt[z]) z^7 - 2917138432 z^(15/2) - 2917138432 E^(4 Sqrt[z]) z^(15/2) + 11769217024 z^8 - 11769217024 E^(4 Sqrt[z]) z^8 + 33554432 z^(17/2) + 33554432 E^(4 Sqrt[z]) z^(17/2) - 134217728 z^9 + 134217728 E^(4 Sqrt[z]) z^9 - 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (347985 - 22496 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 524288 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (347985 - 22496 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]