Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af1w)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.af1w.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), 21/4}, z] == (1/(348798320640 z^(17/4))) ((17 (4 z^(1/4) (-1012042268362125 - 1349389691149500 Sqrt[z] - 1079511752919600 z - 616863858811200 z^(3/2) - 274161715027200 z^2 - 99695169100800 z^(5/2) - 30675436646400 z^3 - 8180116439040 z^(7/2) - 1922168586240 z^4 - 400077619200 z^(9/2) - 72430387200 z^5 - 10758389760 z^(11/2) - 1157627904 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-1012042268362125 + 1349389691149500 Sqrt[z] - 1079511752919600 z + 616863858811200 z^(3/2) - 274161715027200 z^2 + 99695169100800 z^(5/2) - 30675436646400 z^3 + 8180116439040 z^(7/2) - 1922168586240 z^4 + 400077619200 z^(9/2) - 72430387200 z^5 + 10758389760 z^(11/2) - 1157627904 z^6 + 67108864 z^(13/2))) + 1012042268362125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erf[Sqrt[2] z^(1/4)] + 1012042268362125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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/> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1012042268362125 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </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]