Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8ht)

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`=-5/2

http://functions.wolfram.com/07.22.03.a8ht.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(5/2), 15/4}, -z] == -((1/(241591910400 z^(11/4))) (77 (Sqrt[Pi] (2565660825 + 1675533600 z + 1314144000 z^2 - 2156544000 z^3 + 575078400 z^4 - 81788928 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (855220275 + 167553360 z - 146280960 z^2 + 37330944 z^3 - 5308416 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (-2565660825 + 1061171280 z - 221944320 z^2 + 44605440 z^3 - 6094848 z^4 + 1048576 z^5) Sin[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]