Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8980)

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`=7/2

http://functions.wolfram.com/07.22.03.8980.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 3/4}, z] == (1/(2595613870080 z^(5/2))) ((-4 (1578868200 + 3157736400 Sqrt[z] - 1503684000 z - 7217683200 z^(3/2) + 33682521600 z^2 - 246340362240 z^(5/2) - 65405783205 z^3 + 295962603300 z^(7/2) + 13624934400 z^4 - 56627585280 z^(9/2) - 752693760 z^5 + 3049912320 z^(11/2) + 13271040 z^6 - 53280768 z^(13/2) - 65536 z^7 + 262144 z^(15/2) + E^(4 Sqrt[z]) (-1578868200 + 3157736400 Sqrt[z] + 1503684000 z - 7217683200 z^(3/2) - 33682521600 z^2 - 246340362240 z^(5/2) + 65405783205 z^3 + 295962603300 z^(7/2) - 13624934400 z^4 - 56627585280 z^(9/2) + 752693760 z^5 + 3049912320 z^(11/2) - 13271040 z^6 - 53280768 z^(13/2) + 65536 z^7 + 262144 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (1145835402075 - 1222224428880 z + 228720360960 z^2 - 12239216640 z^3 + 213319680 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-1145835402075 + 1222224428880 z - 228720360960 z^2 + 12239216640 z^3 - 213319680 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]