Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa7c)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.aa7c.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(9/2), 23/4}, z] == (209 (4 z^(1/4) (-71176803823125 - 94902405097500 Sqrt[z] - 63610260714000 z - 26968405464000 z^(3/2) - 7505974694400 z^2 - 1316172748800 z^(5/2) - 126705868800 z^3 + 682393600 z^(7/2) - 447283200 z^4 + 1748238336 z^(9/2) - 13631488 z^5 + 54525952 z^(11/2) + E^(4 Sqrt[z]) (71176803823125 - 94902405097500 Sqrt[z] + 63610260714000 z - 26968405464000 z^(3/2) + 7505974694400 z^2 - 1316172748800 z^(5/2) + 126705868800 z^3 + 682393600 z^(7/2) + 447283200 z^4 + 1748238336 z^(9/2) + 13631488 z^5 + 54525952 z^(11/2))) + 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (5475138755625 - 947051028000 z + 104358240000 z^2 - 10967040000 z^3 + 1754726400 z^4 + 534773760 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (5475138755625 - 947051028000 z + 104358240000 z^2 - 10967040000 z^3 + 1754726400 z^4 + 534773760 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (13194139533312 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]