Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8291)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8291.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(15/4)}, -z] == (1/(36182396250 Sqrt[z])) (16 Sqrt[z] (379053675 - 43243200 z + 6531840 z^2 - 1966080 z^3 + 2293760 z^4 + 65536 z^5) Cos[2 Sqrt[z]] + 524288 Sqrt[Pi] z^(21/4) (575 + 16 z) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (15058768725 - 2043241200 z + 252806400 z^2 - 51179520 z^3 + 26542080 z^4 - 149946368 z^5 - 4194304 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]