Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8996)

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`=7/2

http://functions.wolfram.com/07.22.03.8996.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 19/4}, z] == (-4 z^(1/4) (61142922890124075 + 81523897186832100 Sqrt[z] + 27686242058005440 z + 495813279307207680 z^(3/2) + 995493662392320 z^2 + 786455891440128000 z^(5/2) + 496954618288128000 z^3 - 2282089097789964288 z^(7/2) - 119395998660427776 z^4 + 499006684710567936 z^(9/2) + 7705913305595904 z^5 - 31344957679730688 z^(11/2) - 179015981727744 z^6 + 720725845475328 z^(13/2) + 1568736804864 z^7 - 6287832121344 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-61142922890124075 + 81523897186832100 Sqrt[z] - 27686242058005440 z + 495813279307207680 z^(3/2) - 995493662392320 z^2 + 786455891440128000 z^(5/2) - 496954618288128000 z^3 - 2282089097789964288 z^(7/2) + 119395998660427776 z^4 + 499006684710567936 z^(9/2) - 7705913305595904 z^5 - 31344957679730688 z^(11/2) + 179015981727744 z^6 + 720725845475328 z^(13/2) - 1568736804864 z^7 - 6287832121344 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-61142922890124075 + 800416445107078800 z + 2439364404135859200 z^2 + 4336647829574860800 z^3 - 9461777082708787200 z^4 + 2018512444311207936 z^5 - 125911107637346304 z^6 + 2887593486188544 z^7 - 25164213387264 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-61142922890124075 + 800416445107078800 z + 2439364404135859200 z^2 + 4336647829574860800 z^3 - 9461777082708787200 z^4 + 2018512444311207936 z^5 - 125911107637346304 z^6 + 2887593486188544 z^7 - 25164213387264 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(38004806880809975808 z^(15/4))

Standard Form

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MathML Form

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</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> 25164213387264 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2887593486188544 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 125911107637346304 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2018512444311207936 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9461777082708787200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + 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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]