Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8182)

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`=-3/2

http://functions.wolfram.com/07.22.03.8182.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(3/2), 21/4}, z] == (17 (-4 z^(1/4) (784659223228505625 + 1046212297638007500 Sqrt[z] + 417085303941306000 z - 81577566638568000 z^(3/2) - 58519579966848000 z^2 + 57090945719808000 z^(5/2) - 1959269824512000 z^3 - 61361428281753600 z^(7/2) + 9363676092825600 z^4 - 57669657860505600 z^(9/2) + 3943013548032000 z^5 - 32254813274112000 z^(11/2) - 7186341628477440 z^6 + 30438039968808960 z^(13/2) + 605831980646400 z^7 - 2460951836098560 z^(15/2) - 12777527705600 z^8 + 51316269252608 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (784659223228505625 - 1046212297638007500 Sqrt[z] + 417085303941306000 z + 81577566638568000 z^(3/2) - 58519579966848000 z^2 - 57090945719808000 z^(5/2) - 1959269824512000 z^3 + 61361428281753600 z^(7/2) + 9363676092825600 z^4 + 57669657860505600 z^(9/2) + 3943013548032000 z^5 + 32254813274112000 z^(11/2) - 7186341628477440 z^6 - 30438039968808960 z^(13/2) + 605831980646400 z^7 + 2460951836098560 z^(15/2) - 12777527705600 z^8 - 51316269252608 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (784659223228505625 - 419884534169100000 z + 176793488071200000 z^2 - 100575850991616000 z^3 + 256011257069568000 z^4 + 234067435035033600 z^5 + 148614244466688000 z^6 - 123523527868416000 z^7 + 9881882229473280 z^8 - 205471235440640 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (784659223228505625 - 419884534169100000 z + 176793488071200000 z^2 - 100575850991616000 z^3 + 256011257069568000 z^4 + 234067435035033600 z^5 + 148614244466688000 z^6 - 123523527868416000 z^7 + 9881882229473280 z^8 - 205471235440640 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (23939446769241292800 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]