Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9044)

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/07.22.03.9044.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 19/4}, z] == (-4 z^(1/4) (244008853269465375 + 1914685907308492500 Sqrt[z] - 177607439579606400 z + 2773839169572307200 z^(3/2) - 133327883025792000 z^2 + 2699264466830131200 z^(5/2) + 1199337049593446400 z^3 - 5362555016019640320 z^(7/2) - 221975009846231040 z^4 + 920962995860275200 z^(9/2) + 11762327586078720 z^5 - 47728373111193600 z^(11/2) - 232299681546240 z^6 + 934469456363520 z^(13/2) + 1771674009600 z^7 - 7099580940288 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-244008853269465375 + 1914685907308492500 Sqrt[z] + 177607439579606400 z + 2773839169572307200 z^(3/2) + 133327883025792000 z^2 + 2699264466830131200 z^(5/2) - 1199337049593446400 z^3 - 5362555016019640320 z^(7/2) + 221975009846231040 z^4 + 920962995860275200 z^(9/2) - 11762327586078720 z^5 - 47728373111193600 z^(11/2) + 232299681546240 z^6 + 934469456363520 z^(13/2) - 1771674009600 z^7 - 7099580940288 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (2140002301154342625 + 9338191859582586000 z + 12196822020679296000 z^2 + 13798424912283648000 z^3 - 22077479859653836800 z^4 + 3718312397415383040 z^5 - 191603859448135680 z^6 + 3743176741355520 z^7 - 28411208663040 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2140002301154342625 + 9338191859582586000 z + 12196822020679296000 z^2 + 13798424912283648000 z^3 - 22077479859653836800 z^4 + 3718312397415383040 z^5 - 191603859448135680 z^6 + 3743176741355520 z^7 - 28411208663040 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(95012017202024939520 z^(15/4))

Standard Form

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MathML Form

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<msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 68719476736 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 28411208663040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3743176741355520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 191603859448135680 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3718312397415383040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 22077479859653836800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> 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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]