Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6315)

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=1, b₁>=-23/4

For fixed z and a₁=1, b₁=-15/4

http://functions.wolfram.com/07.22.03.6315.01

Input Form

HypergeometricPFQ[{1}, {-(15/4), 19/4}, -z] == (1/(128 z^(15/4))) (4 z^(3/4) (-675675 + 102960 z - 5760 z^2 + 32 z^3) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((2027025 - 3783780 z + 831600 z^2 - 40320 z^3 + 256 z^4) Cos[2 Sqrt[z]] + 18 Sqrt[z] (225225 - 120120 z + 12320 z^2 - 256 z^3) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (18 Sqrt[z] (-225225 + 120120 z - 12320 z^2 + 256 z^3) Cos[2 Sqrt[z]] + (2027025 - 3783780 z + 831600 z^2 - 40320 z^3 + 256 z^4) 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]