Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8948)

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`=5/2

http://functions.wolfram.com/07.22.03.8948.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 19/4}, z] == (-4 z^(1/4) (-9861761756471625 - 13149015675295500 Sqrt[z] + 15300672785798400 z + 28415535173625600 z^(3/2) + 14841718114728960 z^2 + 152088818515845120 z^(5/2) + 166660039036108800 z^3 - 800280950033940480 z^(7/2) - 56973312112066560 z^4 + 240763792922247168 z^(9/2) + 4702590914789376 z^5 - 19194609401856000 z^(11/2) - 132632146870272 z^6 + 534581694431232 z^(13/2) + 1365799600128 z^7 - 5476083302400 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (9861761756471625 - 13149015675295500 Sqrt[z] - 15300672785798400 z + 28415535173625600 z^(3/2) - 14841718114728960 z^2 + 152088818515845120 z^(5/2) - 166660039036108800 z^3 - 800280950033940480 z^(7/2) + 56973312112066560 z^4 + 240763792922247168 z^(9/2) - 4702590914789376 z^5 - 19194609401856000 z^(11/2) + 132632146870272 z^6 + 534581694431232 z^(13/2) - 1365799600128 z^7 - 5476083302400 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (9861761756471625 - 25819885326034800 z + 236067522980889600 z^2 + 979243058291097600 z^3 - 3357404771283763200 z^4 + 976699569828003840 z^5 - 77171324035792896 z^6 + 2142408070397952 z^7 - 21917218111488 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (9861761756471625 - 25819885326034800 z + 236067522980889600 z^2 + 979243058291097600 z^3 - 3357404771283763200 z^4 + 976699569828003840 z^5 - 77171324035792896 z^6 + 2142408070397952 z^7 - 21917218111488 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(12259615122841927680 z^(15/4))

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]