Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7665)

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/07.22.03.7665.01

Input Form

HypergeometricPFQ[{6}, {-(23/4), -(5/4)}, -z] == (1/113565375) (3 (37855125 - 31600800 z + 93139200 z^2 - 68710740 z^3 - 27732320 z^4 - 5585920 z^5 + 98304 z^6) - Sqrt[Pi] z^(9/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-353296125 - 20706000 z + 12180000 z^2 - 3712000 z^3 + 8192 z^4) Cos[2 Sqrt[z]] + 145 (2436525 - 3105900 z - 1140720 z^2 - 243200 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) - Sqrt[Pi] z^(9/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-145 (2436525 - 3105900 z - 1140720 z^2 - 243200 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-353296125 - 20706000 z + 12180000 z^2 - 3712000 z^3 + 8192 z^4) 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]