Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8r1)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8r1.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 11/4}, -z] == (1/(127587778560 z^(7/2))) (7 (Sqrt[Pi] z^(7/4) (-3416695425 + 8282898000 z + 17670182400 z^2 + 2976030720 z^3 + 115015680 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-50544000 - 148262400 z + 370682325 z^2 + 1072293120 z^3 + 184680960 z^4 + 7176192 z^5 + 65536 z^6) Cos[2 Sqrt[z]] + (101088000 + 161740800 z - 33774975 z^2 + 954383040 z^3 + 179504640 z^4 + 7127040 z^5 + 65536 z^6) Sin[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]