Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7661)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-23/4

http://functions.wolfram.com/07.22.03.7661.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(13/4)}, -z] == (1/13287148875) (13287148875 - 4266108000 z + 1397088000 z^2 - 794787840 z^3 + 2601123840 z^4 - 795352320 z^5 + 701972480 z^6 - 5832704 z^7 + 64 Sqrt[Pi] z^(17/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((55769175 - 38949900 z + 22661760 z^2 - 183296 z^3) Cos[2 Sqrt[z]] + 2 Sqrt[z] (55769175 + 35409000 z - 1517056 z^2 + 2048 z^3) Sin[2 Sqrt[z]]) + 64 Sqrt[Pi] z^(17/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (55769175 + 35409000 z - 1517056 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + (-55769175 + 38949900 z - 22661760 z^2 + 183296 z^3) 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]