Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6853)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-19/4

http://functions.wolfram.com/07.22.03.6853.01

Input Form

HypergeometricPFQ[{3}, {-(19/4), 23/4}, -z] == (1/(16384 z^(19/4))) (4 z^(3/4) (-36010099125 + 8519682600 z - 832431600 z^2 + 35418240 z^3 - 609536 z^4 + 2048 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((108030297375 - 210753843300 z + 61491830400 z^2 - 6235669440 z^3 + 272067840 z^4 - 4776960 z^5 + 16384 z^6) Cos[2 Sqrt[z]] + 2 Sqrt[z] (108030297375 - 66713446800 z + 10951340400 z^2 - 721543680 z^3 + 20570880 z^4 - 192512 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-108030297375 + 66713446800 z - 10951340400 z^2 + 721543680 z^3 - 20570880 z^4 + 192512 z^5) Cos[2 Sqrt[z]] + (108030297375 - 210753843300 z + 61491830400 z^2 - 6235669440 z^3 + 272067840 z^4 - 4776960 z^5 + 16384 z^6) 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]