Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9654)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9654.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 5/4}, z] == (1/(6009898752000 z^(9/2))) ((2 (60658723125 + 121317446250 Sqrt[z] + 71990572500 z - 17775450000 z^(3/2) - 22041558000 z^2 + 22752576000 z^(5/2) - 1769644800 z^3 - 56628633600 z^(7/2) + 509657702400 z^4 + 166656298050 z^(9/2) - 753055756200 z^5 - 33953950080 z^(11/2) + 140798883840 z^6 + 1755171840 z^(13/2) - 7105351680 z^7 - 28672000 z^(15/2) + 115081216 z^8 + 131072 z^(17/2) - 524288 z^9 + E^(4 Sqrt[z]) (-60658723125 + 121317446250 Sqrt[z] - 71990572500 z - 17775450000 z^(3/2) + 22041558000 z^2 + 22752576000 z^(5/2) + 1769644800 z^3 - 56628633600 z^(7/2) - 509657702400 z^4 + 166656298050 z^(9/2) + 753055756200 z^5 - 33953950080 z^(11/2) - 140798883840 z^6 + 1755171840 z^(13/2) + 7105351680 z^7 - 28672000 z^(15/2) - 115081216 z^8 + 131072 z^(17/2) + 524288 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (1223854545375 - 1554101010000 z + 284178470400 z^2 - 14253465600 z^3 + 230359040 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (1223854545375 - 1554101010000 z + 284178470400 z^2 - 14253465600 z^3 + 230359040 z^4 - 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule 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]