Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8993)

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`=7/2

http://functions.wolfram.com/07.22.03.8993.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 15/4}, -z] == (Sqrt[Pi] (5558447535465825 - 33880061168553600 z + 90346829782809600 z^2 + 262827141186355200 z^3 + 70087237649694720 z^4 + 5246296151556096 z^5 + 140369127800832 z^6 + 1398011854848 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-1458310758211125 + 3753052444093680 z + 15720119331598080 z^2 + 4322357206659072 z^3 + 326283715215360 z^4 + 8756797636608 z^5 + 87325409280 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (1063805671266975 - 807414461577360 z + 13283392884652800 z^2 + 4102695605514240 z^3 + 319982439038976 z^4 + 8692146634752 z^5 + 87124082688 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (247427128130273280 z^(11/4))

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]