Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7794)

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=-11/4

http://functions.wolfram.com/07.22.03.7794.01

Input Form

HypergeometricPFQ[{6}, {-(11/4), 15/4}, z] == (1/(15728640 z^(11/4))) ((-48 E^(2 Sqrt[z]) z^(3/4) (1091475 + 680400 z + 49360 z^2 - 190976 z^3 + 28672 z^4) - E^(4 Sqrt[z]) Sqrt[2 Pi] (9823275 - 19646550 Sqrt[z] + 22963500 z - 19731600 z^(3/2) + 15271200 z^2 - 11219040 z^(5/2) + 3084480 z^3 + 4435200 z^(7/2) - 4515840 z^4 + 737280 z^(9/2) + 704512 z^5 + 65536 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (9823275 + 19646550 Sqrt[z] + 22963500 z + 19731600 z^(3/2) + 15271200 z^2 + 11219040 z^(5/2) + 3084480 z^3 - 4435200 z^(7/2) - 4515840 z^4 - 737280 z^(9/2) + 704512 z^5 - 65536 z^(11/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 9823275 </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]