Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8fc)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a8fc.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 23/4}, z] == (209 (4 z^(1/4) (-74949174425750625 - 99932232567667500 Sqrt[z] - 62660210691078000 z - 22635872499240000 z^(3/2) - 4532389877433600 z^2 - 402717851827200 z^(5/2) - 13152222720000 z^3 + 32078592000000 z^(7/2) - 4713917644800 z^4 + 17411130261504 z^(9/2) - 417623703552 z^5 + 1619861176320 z^(11/2) - 15955132416 z^6 + 63015223296 z^(13/2) - 268435456 z^7 + 1073741824 z^(15/2) + E^(4 Sqrt[z]) (74949174425750625 - 99932232567667500 Sqrt[z] + 62660210691078000 z - 22635872499240000 z^(3/2) + 4532389877433600 z^2 - 402717851827200 z^(5/2) + 13152222720000 z^3 + 32078592000000 z^(7/2) + 4713917644800 z^4 + 17411130261504 z^(9/2) + 417623703552 z^5 + 1619861176320 z^(11/2) + 15955132416 z^6 + 63015223296 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (74949174425750625 - 17285575363056000 z + 2666645235072000 z^2 - 420357869568000 z^3 + 112095431884800 z^4 + 68324834672640 z^5 + 6430572675072 z^6 + 251255586816 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (74949174425750625 - 17285575363056000 z + 2666645235072000 z^2 - 420357869568000 z^3 + 112095431884800 z^4 + 68324834672640 z^5 + 6430572675072 z^6 + 251255586816 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(106397541196627968 z^(19/4))

Standard Form

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MathML Form

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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]