Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9471)

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`=3/2

http://functions.wolfram.com/07.22.03.9471.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, 13/4}, -z] == (Sqrt[Pi] (-206239658625 - 1539922784400 z + 73916293651200 z^2 + 131406744268800 z^3 + 33373141401600 z^4 + 2240434667520 z^5 + 46858764288 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((206239658625 + 1319933815200 z + 6686560177920 z^2 + 1964803276800 z^3 + 137343467520 z^4 + 2912944128 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-68746552875 + 3660099458400 z + 7872349443840 z^2 + 2060724879360 z^3 + 139484921856 z^4 + 2925527040 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (98107454914560 z^(9/4))

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]