Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8988)

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/07.22.03.8988.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 11/4}, z] == (-4 (12934088294400 + 25868176588800 Sqrt[z] + 28484690127075 z + 198937130055300 z^(3/2) + 292672903592160 z^2 - 1454724261970560 z^(5/2) - 126250536625920 z^3 + 538578544573440 z^(7/2) + 12439890247680 z^4 - 50932601782272 z^(9/2) - 406819897344 z^5 + 1641394470912 z^(11/2) + 4762632192 z^6 - 19100860416 z^(13/2) - 16777216 z^7 + 67108864 z^(15/2) + E^(4 Sqrt[z]) (-12934088294400 + 25868176588800 Sqrt[z] - 28484690127075 z + 198937130055300 z^(3/2) - 292672903592160 z^2 - 1454724261970560 z^(5/2) + 126250536625920 z^3 + 538578544573440 z^(7/2) - 12439890247680 z^4 - 50932601782272 z^(9/2) + 406819897344 z^5 + 1641394470912 z^(11/2) - 4762632192 z^6 - 19100860416 z^(13/2) + 16777216 z^7 + 67108864 z^(15/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (264687977879325 + 1411669215356400 z - 6160011121555200 z^2 + 2190226176552960 z^3 - 204933443420160 z^4 + 6579802865664 z^5 - 76453773312 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (264687977879325 + 1411669215356400 z - 6160011121555200 z^2 + 2190226176552960 z^3 - 204933443420160 z^4 + 6579802865664 z^5 - 76453773312 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(21263268823695360 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]