Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7713)

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=-19/4

http://functions.wolfram.com/07.22.03.7713.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), 3/4}, -z] == (1/126403200) (4 (31600800 - 12563775 z - 25914420 z^2 - 5145840 z^3 - 834048 z^4 + 4096 z^5) + Sqrt[Pi] z^(1/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((197358525 - 175429800 z - 206060400 z^2 - 39070080 z^3 - 6881280 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 210 Sqrt[z] (1879605 + 835380 z - 180336 z^2 - 60928 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) - Sqrt[Pi] z^(1/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-210 Sqrt[z] (1879605 + 835380 z - 180336 z^2 - 60928 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + (197358525 - 175429800 z - 206060400 z^2 - 39070080 z^3 - 6881280 z^4 + 32768 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]