Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8082)

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`=-7/2

http://functions.wolfram.com/07.22.03.8082.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), 17/4}, z] == (13 (-4 z^(1/4) (-13928861950801875 - 18571815934402500 Sqrt[z] - 6603312332232000 z + 2515547555136000 z^(3/2) + 437486531328000 z^2 - 2465833176576000 z^(5/2) + 345218601369600 z^3 - 1254319511961600 z^(7/2) + 68600925388800 z^4 - 256443560755200 z^(9/2) + 9013831925760 z^5 - 35219570688000 z^(11/2) + 1075084001280 z^6 - 5077456650240 z^(13/2) - 273804165120 z^7 + 1108101562368 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-13928861950801875 + 18571815934402500 Sqrt[z] - 6603312332232000 z - 2515547555136000 z^(3/2) + 437486531328000 z^2 + 2465833176576000 z^(5/2) + 345218601369600 z^3 + 1254319511961600 z^(7/2) + 68600925388800 z^4 + 256443560755200 z^(9/2) + 9013831925760 z^5 + 35219570688000 z^(11/2) + 1075084001280 z^6 + 5077456650240 z^(13/2) - 273804165120 z^7 - 1108101562368 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-13928861950801875 + 8254140415290000 z - 4593608578944000 z^2 + 9026037909504000 z^3 + 4813886885068800 z^4 + 1000288183910400 z^5 + 138568060108800 z^6 + 21115132968960 z^7 - 4445291151360 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-13928861950801875 + 8254140415290000 z - 4593608578944000 z^2 + 9026037909504000 z^3 + 4813886885068800 z^4 + 1000288183910400 z^5 + 138568060108800 z^6 + 21115132968960 z^7 - 4445291151360 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (581861553419059200 z^(13/4))

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> 4445291151360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21115132968960 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 138568060108800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1000288183910400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4813886885068800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> 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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]