Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8059)

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`=-7/2

http://functions.wolfram.com/07.22.03.8059.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), -(7/4)}, -z] == (1/33075) ((33075 - 35100 z - 720 z^2 + 4650 z^3 + 10560 z^4 + 512 z^5) Cos[2 Sqrt[z]] + Sqrt[Pi] z^(11/4) (-98325 + 104880 z + 88320 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 Sqrt[z] (33075 + 9000 z + 23040 z^2 - 22500 z^3 - 21888 z^4 - 1024 z^5) 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]