Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8e1)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8e1.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 23/4}, -z] == -((19 (Sqrt[Pi] (341435127939530625 + 71062920937008000 z + 9777699195264000 z^2 + 1354486468608000 z^3 + 311376199680000 z^4 - 159424614236160 z^5 + 12146637275136 z^6 - 362924736512 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (113811709313176875 - 28340569659402000 z + 839197085126400 z^2 + 21706513920000 z^3 - 10116366532608 z^4 + 763527954432 z^5 - 22733127680 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-341435127939530625 + 293134548865158000 z - 26471845701100800 z^2 + 173197308211200 z^3 - 10768343040000 z^4 + 781420855296 z^5 - 22934454272 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (5910974510923776 z^(19/4)))

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]