Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6541)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-21/4

http://functions.wolfram.com/07.22.03.6541.01

Input Form

HypergeometricPFQ[{2}, {-(21/4), 21/4}, -z] == (1/(10752 z^(17/4))) (2 z^(1/4) (8511477975 - 2784321540 z + 402642240 z^2 - 20180160 z^3 + 351744 z^4 - 1024 z^5) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-8511477975 + 5054049000 z - 741620880 z^2 + 38712960 z^3 - 689920 z^4 + 2048 z^5) Cos[2 Sqrt[z]] + (8511477975 - 16402686300 z + 4454049600 z^2 - 383423040 z^3 + 12038400 z^4 - 105472 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-8511477975 + 16402686300 z - 4454049600 z^2 + 383423040 z^3 - 12038400 z^4 + 105472 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-8511477975 + 5054049000 z - 741620880 z^2 + 38712960 z^3 - 689920 z^4 + 2048 z^5) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]