Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7757)

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=-15/4

http://functions.wolfram.com/07.22.03.7757.01

Input Form

HypergeometricPFQ[{6}, {-(15/4), 11/4}, -z] == (1/(40550400 z^(7/4))) (-4 z^(3/4) (-6081075 - 2134800 z + 6709680 z^2 + 1026048 z^3 + 126976 z^4) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (3 (6081075 - 18427500 z + 1965600 z^2 + 17559360 z^3 + 2529280 z^4 + 344064 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (18243225 - 30958200 z - 28894320 z^2 + 5616000 z^3 + 1597440 z^4 - 32768 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-18243225 + 30958200 z + 28894320 z^2 - 5616000 z^3 - 1597440 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 3 (6081075 - 18427500 z + 1965600 z^2 + 17559360 z^3 + 2529280 z^4 + 344064 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]