Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9040)

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/07.22.03.9040.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 15/4}, z] == (-4 (4138908254208000 + 8277816508416000 Sqrt[z] + 1373977486893375 z + 34943236016188500 z^(3/2) - 170981952850800 z^2 + 52474341436171200 z^(5/2) + 32279077586246400 z^3 - 147978599719910400 z^(7/2) - 7640338477363200 z^4 + 31920480834600960 z^(9/2) + 488661967503360 z^5 - 1987503284551680 z^(11/2) - 11281005281280 z^6 + 45416448000000 z^(13/2) + 98398371840 z^7 - 394398793728 z^(15/2) - 268435456 z^8 + 1073741824 z^(17/2) + E^(4 Sqrt[z]) (-4138908254208000 + 8277816508416000 Sqrt[z] - 1373977486893375 z + 34943236016188500 z^(3/2) + 170981952850800 z^2 + 52474341436171200 z^(5/2) - 32279077586246400 z^3 - 147978599719910400 z^(7/2) + 7640338477363200 z^4 + 31920480834600960 z^(9/2) - 488661967503360 z^5 - 1987503284551680 z^(11/2) + 11281005281280 z^6 + 45416448000000 z^(13/2) - 98398371840 z^7 - 394398793728 z^(15/2) + 268435456 z^8 + 1073741824 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (64848554580434625 + 169400305842768000 z + 287467185672576000 z^2 - 613263329434828800 z^3 + 129108069354700800 z^4 - 7983494143672320 z^5 + 181959980482560 z^6 - 1578400481280 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (64848554580434625 + 169400305842768000 z + 287467185672576000 z^2 - 613263329434828800 z^3 + 129108069354700800 z^4 - 7983494143672320 z^5 + 181959980482560 z^6 - 1578400481280 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (2474271281302732800 z^(7/2))

Standard Form

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MathML 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]