Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8510)

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/07.22.03.8510.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 13/4}, z] == (-4 (-32821956034560000 - 65643912069120000 Sqrt[z] + 11253242068992000 z + 110031700230144000 z^(3/2) - 437125936368844800 z^2 + 230973930096473025 z^(5/2) - 780348303965884500 z^3 + 350589070104966000 z^(7/2) - 1910300529298392000 z^4 - 238349262898010880 z^(9/2) + 1029765656673008640 z^5 + 28952561607782400 z^(11/2) - 119182617885327360 z^6 - 1186526373150720 z^(13/2) + 4802868037287936 z^7 + 19346014339072 z^(15/2) - 77760236093440 z^8 - 126315659264 z^(17/2) + 506067943424 z^9 + 268435456 z^(19/2) - 1073741824 z^10 + E^(4 Sqrt[z]) (32821956034560000 - 65643912069120000 Sqrt[z] - 11253242068992000 z + 110031700230144000 z^(3/2) + 437125936368844800 z^2 + 230973930096473025 z^(5/2) + 780348303965884500 z^3 + 350589070104966000 z^(7/2) + 1910300529298392000 z^4 - 238349262898010880 z^(9/2) - 1029765656673008640 z^5 + 28952561607782400 z^(11/2) + 119182617885327360 z^6 - 1186526373150720 z^(13/2) - 4802868037287936 z^7 + 19346014339072 z^(15/2) + 77760236093440 z^8 - 126315659264 z^(17/2) - 506067943424 z^9 + 268435456 z^(19/2) + 1073741824 z^10)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1275274794098930625 + 2511310363764048000 z + 8272551786516864000 z^2 - 4201931066167296000 z^3 + 480220693276262400 z^4 - 19269043491962880 z^5 + 311418884718592 z^6 - 2025077080064 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (1275274794098930625 + 2511310363764048000 z + 8272551786516864000 z^2 - 4201931066167296000 z^3 + 480220693276262400 z^4 - 19269043491962880 z^5 + 311418884718592 z^6 - 2025077080064 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (30143780256900710400 z^(9/2))

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]