Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6805)

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=-23/4

http://functions.wolfram.com/07.22.03.6805.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), 15/4}, -z] == (1/(839040 z^(11/4))) (-12 z^(3/4) (80405325 - 24324300 z + 3390160 z^2 - 236672 z^3 + 5376 z^4) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-723647925 + 494594100 z - 105945840 z^2 + 11088000 z^3 - 503040 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + (723647925 - 1459458000 z + 508107600 z^2 - 74511360 z^3 + 5402880 z^4 - 126976 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-723647925 + 1459458000 z - 508107600 z^2 + 74511360 z^3 - 5402880 z^4 + 126976 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-723647925 + 494594100 z - 105945840 z^2 + 11088000 z^3 - 503040 z^4 + 4096 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]