Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8dt)

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.a8dt.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(11/2), 15/4}, -z] == (1/(386547056640 z^(11/4))) ((-Sqrt[Pi]) (1364076338625 + 566888868000 z + 260638560000 z^2 - 222411571200 z^3 + 25418465280 z^4 - 1063256064 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (454692112875 - 18896295600 z - 14228513280 z^2 + 1601544192 z^3 - 66650112 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (-1364076338625 + 888125893200 z - 25484659200 z^2 + 1654824960 z^3 - 67436544 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]