Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7525)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-9/4

http://functions.wolfram.com/07.22.03.7525.01

Input Form

HypergeometricPFQ[{5}, {-(9/4), 21/4}, -z] == (1/(6291456 z^(17/4))) (221 (2 z^(1/4) (-79053975 + 34428240 z - 7176960 z^2 + 860160 z^3 - 96768 z^4 + 8192 z^5) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-79053975 + 55509300 z - 12610080 z^2 + 1542720 z^3 - 174080 z^4 + 16384 z^5) Cos[2 Sqrt[z]] + (79053975 - 160914600 z + 58514400 z^2 - 9327360 z^3 + 983040 z^4 - 131072 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-79053975 + 160914600 z - 58514400 z^2 + 9327360 z^3 - 983040 z^4 + 131072 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-79053975 + 55509300 z - 12610080 z^2 + 1542720 z^3 - 174080 z^4 + 16384 z^5) Sin[2 Sqrt[z]])))

Standard Form

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MathML Form

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/> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]