Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7491)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-13/4

http://functions.wolfram.com/07.22.03.7491.01

Input Form

HypergeometricPFQ[{5}, {-(13/4), 21/4}, -z] == (1/(3145728 z^(17/4))) (17 (2 z^(1/4) (-1185809625 + 510810300 z - 104615280 z^2 + 11975040 z^3 - 1120512 z^4 + 102400 z^5) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((1185809625 - 2408105700 z + 865695600 z^2 - 134386560 z^3 + 13052160 z^4 - 1351680 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 6 Sqrt[z] (-395269875 + 275675400 z - 61538400 z^2 + 7223040 z^3 - 675840 z^4 + 65536 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (6 Sqrt[z] (-395269875 + 275675400 z - 61538400 z^2 + 7223040 z^3 - 675840 z^4 + 65536 z^5) Cos[2 Sqrt[z]] + (1185809625 - 2408105700 z + 865695600 z^2 - 134386560 z^3 + 13052160 z^4 - 1351680 z^5 + 65536 z^6) Sin[2 Sqrt[z]])))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 134386560 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 865695600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2408105700 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1185809625 </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]