Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9068)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9068.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(5/4)}, z] == (-99613755115875 + 99613755115875 E^(4 Sqrt[z]) - 199227510231750 Sqrt[z] - 199227510231750 E^(4 Sqrt[z]) Sqrt[z] - 150967430113500 z + 150967430113500 E^(4 Sqrt[z]) z - 36298179918000 z^(3/2) - 36298179918000 E^(4 Sqrt[z]) z^(3/2) + 12330960642000 z^2 - 12330960642000 E^(4 Sqrt[z]) z^2 + 2223046425600 z^(5/2) + 2223046425600 E^(4 Sqrt[z]) z^(5/2) - 4075585113600 z^3 + 4075585113600 E^(4 Sqrt[z]) z^3 + 2964061900800 z^(7/2) + 2964061900800 E^(4 Sqrt[z]) z^(7/2) - 1886221209600 z^4 + 1886221209600 E^(4 Sqrt[z]) z^4 + 1247920128000 z^(9/2) + 1247920128000 E^(4 Sqrt[z]) z^(9/2) - 953249955840 z^5 + 953249955840 E^(4 Sqrt[z]) z^5 + 940368199680 z^(11/2) + 940368199680 E^(4 Sqrt[z]) z^(11/2) - 1447050608640 z^6 + 1447050608640 E^(4 Sqrt[z]) z^6 + 6299509063680 z^(13/2) + 6299509063680 E^(4 Sqrt[z]) z^(13/2) + 186909327360 z^7 - 186909327360 E^(4 Sqrt[z]) z^7 - 762655014912 z^(15/2) - 762655014912 E^(4 Sqrt[z]) z^(15/2) - 5121245184 z^8 + 5121245184 E^(4 Sqrt[z]) z^8 + 20585644032 z^(17/2) + 20585644032 E^(4 Sqrt[z]) z^(17/2) + 33554432 z^9 - 33554432 E^(4 Sqrt[z]) z^9 - 134217728 z^(19/2) - 134217728 E^(4 Sqrt[z]) z^(19/2) - 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-196383915 + 23390640 z - 628992 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 32768 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (-196383915 + 23390640 z - 628992 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(28119150259200 z^(9/2))

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]