Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8410)

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/07.22.03.8410.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 9/4}, z] == (-4 (23444254310400 + 46888508620800 Sqrt[z] - 468885086208000 z + 512892191421225 z^(3/2) - 3984155269686900 z^2 - 1210918752156960 z^(5/2) + 5582301002974080 z^3 + 305469020102400 z^(7/2) - 1282416006896640 z^4 - 21963337482240 z^(9/2) + 89508961124352 z^5 + 570401685504 z^(11/2) - 2298099793920 z^6 - 5555355648 z^(13/2) + 22271754240 z^7 + 16777216 z^(15/2) - 67108864 z^8 + E^(4 Sqrt[z]) (-23444254310400 + 46888508620800 Sqrt[z] + 468885086208000 z + 512892191421225 z^(3/2) + 3984155269686900 z^2 - 1210918752156960 z^(5/2) - 5582301002974080 z^3 + 305469020102400 z^(7/2) + 1282416006896640 z^4 - 21963337482240 z^(9/2) - 89508961124352 z^5 + 570401685504 z^(11/2) + 2298099793920 z^6 - 5555355648 z^(13/2) - 22271754240 z^7 + 16777216 z^(15/2) + 67108864 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1513180375331625 + 18830689115238000 z - 23176232757216000 z^2 + 5193553559040000 z^3 - 359726653440000 z^4 + 9209002328064 z^5 - 89137348608 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1513180375331625 + 18830689115238000 z - 23176232757216000 z^2 + 5193553559040000 z^3 - 359726653440000 z^4 + 9209002328064 z^5 - 89137348608 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (88020782206156800 z^(5/2))

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]