Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8760)

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`=-3/2

http://functions.wolfram.com/07.22.03.8760.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 23/4}, z] == -((19 (4 z^(1/4) (872777198928009375 + 1163702931904012500 Sqrt[z] + 558577407313926000 z + 35465232210408000 z^(3/2) - 44707686665241600 z^2 + 13756211281612800 z^(5/2) + 7765842180096000 z^3 - 14369772095078400 z^(7/2) + 7303448523571200 z^4 - 18754357053358080 z^(9/2) + 3213544327741440 z^5 - 9664765467033600 z^(11/2) + 1881418141532160 z^6 - 8399993689866240 z^(13/2) - 323008384204800 z^7 + 1320895717048320 z^(15/2) + 9856949944320 z^8 - 39633958207488 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-872777198928009375 + 1163702931904012500 Sqrt[z] - 558577407313926000 z + 35465232210408000 z^(3/2) + 44707686665241600 z^2 + 13756211281612800 z^(5/2) - 7765842180096000 z^3 - 14369772095078400 z^(7/2) - 7303448523571200 z^4 - 18754357053358080 z^(9/2) - 3213544327741440 z^5 - 9664765467033600 z^(11/2) - 1881418141532160 z^6 - 8399993689866240 z^(13/2) + 323008384204800 z^7 + 1320895717048320 z^(15/2) - 9856949944320 z^8 - 39633958207488 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-872777198928009375 + 372384938209284000 z - 116068032688608000 z^2 + 41615429087232000 z^3 - 29877743960064000 z^4 - 63739187114803200 z^5 - 33994233127895040 z^6 - 34533824129925120 z^7 + 5312896019988480 z^8 - 158741991260160 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-872777198928009375 + 372384938209284000 z - 116068032688608000 z^2 + 41615429087232000 z^3 - 29877743960064000 z^4 - 63739187114803200 z^5 - 33994233127895040 z^6 - 34533824129925120 z^7 + 5312896019988480 z^8 - 158741991260160 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (6383852471797678080 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]