Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8c3)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8c3.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 1/4}, -z] == (1/(8121484800 z^(9/2))) (2 Sqrt[z] (-10854718875 + 1216215000 z - 119750400 z^2 - 532224000 z^3 + 1394933760 z^4 + 463242240 z^5 + 24084480 z^6 + 262144 z^7) Cos[2 Sqrt[z]] + 1024 Sqrt[Pi] z^(21/4) (27633375 + 7579440 z + 380160 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - (-10854718875 + 15689173500 z + 2118085200 z^2 + 665280000 z^3 - 1490227200 z^4 + 13495173120 z^5 + 3845038080 z^6 + 194248704 z^7 + 2097152 z^8) 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]