Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8018)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8018.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 1/4}, z] == (1/1857945600) ((4 (232243200 + 464486400 Sqrt[z] - 97399575 z + 351823500 z^(3/2) - 24747840 z^2 + 90723840 z^(5/2) - 3555840 z^3 + 13670400 z^(7/2) - 409600 z^4 + 1835008 z^(9/2) + 65536 z^5 - 262144 z^(11/2) + E^(4 Sqrt[z]) (232243200 - 464486400 Sqrt[z] - 97399575 z - 351823500 z^(3/2) - 24747840 z^2 - 90723840 z^(5/2) - 3555840 z^3 - 13670400 z^(7/2) - 409600 z^4 - 1835008 z^(9/2) + 65536 z^5 + 262144 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (1748906775 + 1332500400 z + 352396800 z^2 + 53698560 z^3 + 7536640 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (1748906775 + 1332500400 z + 352396800 z^2 + 53698560 z^3 + 7536640 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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352396800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1332500400 </cn> <ci> z </ci> </apply> <cn type='integer'> 1748906775 </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]