Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9186)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9186.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 17/4}, z] == (13 (-4 z^(1/4) (-3754736699781375 - 5006315599708500 Sqrt[z] - 2282449262662800 z + 8202872462400 z^(3/2) + 105725911737600 z^2 - 272655747302400 z^(5/2) + 25335886786560 z^3 - 89600587776000 z^(7/2) + 2859605360640 z^4 - 10778148864000 z^(9/2) + 183883530240 z^5 - 709059674112 z^(11/2) + 7902068736 z^6 - 30802968576 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (-3754736699781375 + 5006315599708500 Sqrt[z] - 2282449262662800 z - 8202872462400 z^(3/2) + 105725911737600 z^2 + 272655747302400 z^(5/2) + 25335886786560 z^3 + 89600587776000 z^(7/2) + 2859605360640 z^4 + 10778148864000 z^(9/2) + 183883530240 z^5 + 709059674112 z^(11/2) + 7902068736 z^6 + 30802968576 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-3754736699781375 + 1722603217104000 z - 714561334502400 z^2 + 994172291481600 z^3 + 348832382976000 z^4 + 42524328591360 z^5 + 2811525857280 z^6 + 122406567936 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-3754736699781375 + 1722603217104000 z - 714561334502400 z^2 + 994172291481600 z^3 + 348832382976000 z^4 + 42524328591360 z^5 + 2811525857280 z^6 + 122406567936 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(58186155341905920 z^(13/4))

Standard Form

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MathML Form

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<mrow> <mn> 42524328591360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 348832382976000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 994172291481600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 714561334502400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1722603217104000 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 3754736699781375 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 58186155341905920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> 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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]