Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7990)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7990.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 21/4}, z] == (221 (-4 z^(1/4) (1532439462965271485625 + 2043252617287028647500 Sqrt[z] + 1150992006897781818000 z + 289244890088758296000 z^(3/2) + 9825728750361216000 z^2 + 3572992272858624000 z^(5/2) + 2919864653088768000 z^3 - 8447849011342540800 z^(7/2) + 617730334624972800 z^4 - 2243059352587468800 z^(9/2) + 58416931012608000 z^5 - 222570229845196800 z^(11/2) + 3165630140252160 z^6 - 12282689759477760 z^(13/2) + 113886426562560 z^7 - 445753180815360 z^(15/2) + 3027951943680 z^8 - 11905649344512 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (1532439462965271485625 - 2043252617287028647500 Sqrt[z] + 1150992006897781818000 z - 289244890088758296000 z^(3/2) + 9825728750361216000 z^2 - 3572992272858624000 z^(5/2) + 2919864653088768000 z^3 + 8447849011342540800 z^(7/2) + 617730334624972800 z^4 + 2243059352587468800 z^(9/2) + 58416931012608000 z^5 + 222570229845196800 z^(11/2) + 3165630140252160 z^6 + 12282689759477760 z^(13/2) + 113886426562560 z^7 + 445753180815360 z^(15/2) + 3027951943680 z^8 + 11905649344512 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (1532439462965271485625 - 483610086931841100000 z + 110539448441563680000 z^2 - 30428063226925056000 z^3 + 31555028531625984000 z^4 + 8780529678365491200 z^5 + 880253601841152000 z^6 + 48775957158297600 z^7 + 1773671169392640 z^8 + 47416438947840 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (1532439462965271485625 - 483610086931841100000 z + 110539448441563680000 z^2 - 30428063226925056000 z^3 + 31555028531625984000 z^4 + 8780529678365491200 z^5 + 880253601841152000 z^6 + 48775957158297600 z^7 + 1773671169392640 z^8 + 47416438947840 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(29493398419705272729600 z^(17/4))

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]