Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7693)

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=-21/4

http://functions.wolfram.com/07.22.03.7693.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 5/4}, -z] == (1/(801964800 z^(1/4))) (2 z^(1/4) (-283372425 - 313594740 z + 56236320 z^2 + 21696960 z^3 + 2242560 z^4 - 16384 z^5) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (3 (-228118275 + 138253500 z + 347608800 z^2 + 44268480 z^3 + 583680 z^4 + 507904 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-684354825 - 497712600 z + 135883440 z^2 + 44323200 z^3 + 4669440 z^4 - 32768 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (684354825 + 497712600 z - 135883440 z^2 - 44323200 z^3 - 4669440 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 3 (-228118275 + 138253500 z + 347608800 z^2 + 44268480 z^3 + 583680 z^4 + 507904 z^5) Sin[2 Sqrt[z]]))

Standard Form

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MathML Form

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<times /> <cn type='integer'> 3 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 507904 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 583680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 44268480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 347608800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 138253500 </cn> <ci> z </ci> </apply> <cn type='integer'> -228118275 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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]