Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7388)

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=-23/4

http://functions.wolfram.com/07.22.03.7388.01

Input Form

HypergeometricPFQ[{5}, {-(23/4), 23/4}, z] == (1/(144703488 z^(19/4))) ((-48 E^(2 Sqrt[z]) z^(3/4) (5293484571375 + 1546033589100 z + 202897094400 z^2 + 14936201280 z^3 + 718658816 z^4 + 24038400 z^5 + 376832 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-47641361142375 + 95282722284750 Sqrt[z] - 95585207117400 z + 64126784521800 z^(3/2) - 32373113572800 z^2 + 13122149040000 z^(5/2) - 4451282035200 z^3 + 1300980320640 z^(7/2) - 334979124480 z^4 + 77422625280 z^(9/2) - 16328632320 z^5 + 3167324160 z^(11/2) - 554631168 z^6 + 81985536 z^(13/2) - 8912896 z^7 + 524288 z^(15/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (47641361142375 + 95282722284750 Sqrt[z] + 95585207117400 z + 64126784521800 z^(3/2) + 32373113572800 z^2 + 13122149040000 z^(5/2) + 4451282035200 z^3 + 1300980320640 z^(7/2) + 334979124480 z^4 + 77422625280 z^(9/2) + 16328632320 z^5 + 3167324160 z^(11/2) + 554631168 z^6 + 81985536 z^(13/2) + 8912896 z^7 + 524288 z^(15/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> 81985536 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 554631168 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3167324160 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16328632320 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 77422625280 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 334979124480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1300980320640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4451282035200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13122149040000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32373113572800 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64126784521800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 95585207117400 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 95282722284750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 47641361142375 </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]