Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8949)

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/07.22.03.8949.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 19/4}, -z] == (Sqrt[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) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-3287253918823875 - 7103883793406400 z + 38022204628961280 z^2 + 200070237508485120 z^3 + 60190948230561792 z^4 + 4798652350464000 z^5 + 133645423607808 z^6 + 1369020825600 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (9861761756471625 + 15300672785798400 z - 14841718114728960 z^2 + 166660039036108800 z^3 + 56973312112066560 z^4 + 4702590914789376 z^5 + 132632146870272 z^6 + 1365799600128 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(3064903780710481920 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]