Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8596)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8596.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 3/4}, z] == (1/7431782400) ((4 (928972800 - 219017925 Sqrt[z] + 533729700 z - 41448960 z^(3/2) + 138458880 z^2 - 5214720 z^(5/2) + 18708480 z^3 - 491520 z^(7/2) + 1769472 z^4 - 65536 z^(9/2) + 262144 z^5 + E^(4 Sqrt[z]) (928972800 + 219017925 Sqrt[z] + 533729700 z + 41448960 z^(3/2) + 138458880 z^2 + 5214720 z^(5/2) + 18708480 z^3 + 491520 z^(7/2) + 1769472 z^4 + 65536 z^(9/2) + 262144 z^5)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (2076963525 + 1954789200 z + 534643200 z^2 + 73113600 z^3 + 6881280 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (2076963525 + 1954789200 z + 534643200 z^2 + 73113600 z^3 + 6881280 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</ci> </apply> <cn type='integer'> 2076963525 </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> </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]