Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9036)

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/07.22.03.9036.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 11/4}, z] == (-4 (-24251415552000 - 48502831104000 Sqrt[z] + 64670441472000 z + 194011324416000 z^(3/2) + 56196195339375 z^2 + 718758433329300 z^(5/2) + 718909215242400 z^3 - 3431408022000000 z^(7/2) - 235690099142400 z^4 + 994860481305600 z^(9/2) + 19010545827840 z^5 - 77572676321280 z^(11/2) - 528090071040 z^6 + 2128324853760 z^(13/2) + 5379194880 z^7 - 21567111168 z^(15/2) - 16777216 z^8 + 67108864 z^(17/2) + E^(4 Sqrt[z]) (24251415552000 - 48502831104000 Sqrt[z] - 64670441472000 z + 194011324416000 z^(3/2) - 56196195339375 z^2 + 718758433329300 z^(5/2) - 718909215242400 z^3 - 3431408022000000 z^(7/2) + 235690099142400 z^4 + 994860481305600 z^(9/2) - 19010545827840 z^5 - 77572676321280 z^(11/2) + 528090071040 z^6 + 2128324853760 z^(13/2) - 5379194880 z^7 - 21567111168 z^(15/2) + 16777216 z^8 + 67108864 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (1323439889396625 + 4491674776134000 z - 14373359283628800 z^2 + 4034627167334400 z^3 - 311855239987200 z^4 + 8529374085120 z^5 - 86318776320 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (1323439889396625 + 4491674776134000 z - 14373359283628800 z^2 + 4034627167334400 z^3 - 311855239987200 z^4 + 8529374085120 z^5 - 86318776320 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(53158172059238400 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]