Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8952)

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`=5/2

http://functions.wolfram.com/07.22.03.8952.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 23/4}, z] == (-4 z^(1/4) (1331337837123669375 + 1775117116164892500 Sqrt[z] - 157788188103546000 z - 1292360397800472000 z^(3/2) + 743175535310208000 z^2 + 1923513150214656000 z^(5/2) + 354037253997772800 z^3 + 6583532857742131200 z^(7/2) + 5519225534260838400 z^4 - 25794889783404134400 z^(9/2) - 1533596485917081600 z^5 + 6432801805503037440 z^(11/2) + 107821741815889920 z^6 - 439009742589788160 z^(13/2) - 2655433323970560 z^7 + 10693888746455040 z^(15/2) + 24288040058880 z^8 - 97358318665728 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-1331337837123669375 + 1775117116164892500 Sqrt[z] + 157788188103546000 z - 1292360397800472000 z^(3/2) - 743175535310208000 z^2 + 1923513150214656000 z^(5/2) - 354037253997772800 z^3 + 6583532857742131200 z^(7/2) - 5519225534260838400 z^4 - 25794889783404134400 z^(9/2) + 1533596485917081600 z^5 + 6432801805503037440 z^(11/2) - 107821741815889920 z^6 - 439009742589788160 z^(13/2) + 2655433323970560 z^7 + 10693888746455040 z^(15/2) - 24288040058880 z^8 - 97358318665728 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-1331337837123669375 + 1577881881035460000 z - 2065590826082784000 z^2 + 12590267892314112000 z^3 + 39169722331643904000 z^4 - 107436952681080422400 z^5 + 26045321862080102400 z^6 - 1763915977960980480 z^7 + 42848161407959040 z^8 - 389639433093120 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1331337837123669375 + 1577881881035460000 z - 2065590826082784000 z^2 + 12590267892314112000 z^3 + 39169722331643904000 z^4 - 107436952681080422400 z^5 + 26045321862080102400 z^6 - 1763915977960980480 z^7 + 42848161407959040 z^8 - 389639433093120 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(412955456769412300800 z^(19/4))

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]